The Cortical Changes on Fertilization of the Sea-Urchin Egg

When the sea-urchin egg is fertilized, a change in the optical properties of the cortex spreads over the egg surface from the point of sperm attachment, this change taking about 20 sec. to pass over the egg surface at room temperature in Psammechinus miliaris (Rothschild & Swann, 1949). Rothschild (1949) examined the possibility that this cortical change might be due to a finite amount of a substance, derived directly or indirectly from the sperm head, diffusing round the cortex or through the egg cytoplasm. After comparing the rate at which the cortical change spreads over the egg surface with the appropriate theoretical diffusion curves, he concluded that the diffusion hypothesis could not be rejected, and that the intra-cytoplasmic route was more consistent with the experimental data than the cortical route. He also stated that the hypothesis of a simple diffusion mechanism might be over-simplified, or that the similarity between the theoretical and experimental curves might be fortuitous. There are several considerations which make the diffusion hypothesis difficult to sustain, and it will be shown that an autocatalytic mechanism initiated by the spermatozoon is more consistent with the data. Rothschild & Swann’s raw data, which they were kind enough to allow me to re-examine, do not, however, enable a decision to be made between the intra-cytoplasmic and intracortical pathways.

Rothschild & Swann’s procedure was as follows. Photographs of the egg in optical section, taken at 0·5 sec. intervals, exposure 0·25 sec., show the spreading of a crescent (which appears dark in the negatives) from a certain point in the surface layer. The change reaches completion at a point approximately opposite to the beginning of the change. The rate of change was estimated from frame to frame on slightly enlarged prints by measuring the angle subtended at the centre by the arc.

Two possible sources of error arise from such a procedure. First, the use of prints introduces greater contrasts in optical densities and tends to ‘smear out’ finer details. Secondly, the decision as to where the ‘centre’ of the egg is will determine the angle which is recorded for a particular frame. An error in placing the centre will be negligible for small angles, but becomes important at angles in the neighbourhood of 180°. Thus, for example, an error of 7% in placing the centre can cause an angle of 178° to be read for a true angle of 160°. Since the cross-section of the egg is not perfectly circular this type of error is quite likely to occur. In order to eliminate both these difficulties, the following method was adopted in the re-examination of the material. The original film was used and the image of each frame was projected on to a carefully alined movable paper strip. The magnification resulted in an image of about 6 cm. diameter. The estimated arc was drawn and delimited for each frame. A graduated brass strip was bent into the exact shape of the arc and its length read off. This was then expressed as a fraction of the total circumference, thus avoiding the possible systematic error of the angular measurement.

While the use of prints resulted in the recording of definite arc lengths (or angles), the projection of the original film disclosed no definite end-points, but rather the tailing off of the optical change until it merged with the unchanged surface layer. A further uncertainty arose due to the structure of the egg material which resulted in considerable optical inhomogeneity. As a result each arc length could only be determined as lying between two limits : ‘definitely changed ‘and ‘definitely not changed’. With this procedure the variation between repeated readings (at different times) and between observers was considerable. It is therefore not justifiable to attach numerical significance to individual readings except as a qualitative indication of the rate of change.

A second significant difference between the two methods of measurement arose in determining the beginning of the change. The area where the measurable arc was first visible had shown, many frames previously, distinct changes of shape, structure and optical density. A slight flattening, a fuzziness and increase in grains indicated that something was happening.

A particular set of readings is shown in Fig. 1, together with the points recorded by Rothschild & Swann from print measurements of the same egg. It will be noted that the initial observations are indicated as points, although the observed changes often extended over considerable distances. Only when the optical change was a distinct and progressively increasing crescent were the limits recorded as lengths. In the middle regions the judgement was often extremely variable and often no data were recorded. Similarly, the end-point extended over several frames from ‘probably complete’ to ‘definitely complete’.

In spite of the uncertainties involved, there are certain characteristics of the general shape which are relevant to an interpretation of the mechanism. These are : the long induction period, the position of half completion and the inflexion of the average slope somewhere at this position. In Fig. 2 is given a composite plot from several sets of readings, indicating in a qualitative way the spread of the observations on one egg where the fertilization cone was visible.

There are three main factors determining the observed rate of change: (1) the geometrical properties of the body, (2) the plane of observation relative to the change, and (3) the intrinsic rate of change.

The egg is very nearly a sphere. Calculations based on rotation ellipsoids show that the deviations are negligible compared with the experimental errors and therefore do not justify the more tedious analysis. The fact that the change spreads from a point over (or in) the surface may be due to a change in the surface layer only or to a change in the body of the egg which reacts with the differently constituted surface layer to produce the observed change. These two possibilities were dealt with by Rothschild and will also be considered here.

Arguments have been fairly convincingly advanced in favour of the spreading of some material substance rather than the propagation of an action potential. Consequently, in what follows it will be assumed that some substance is concerned in the propagation of the change, although diffusion will not be considered the only means.

The rate of progress of a substance in the surface layer or through the body of the egg will (apart from quantities involved) be rather different owing to the differences in the rates of increase of the two functions.

The surface area, s, of a spherical cap is given in terms of the radius, r, and the half angle, θ, subtended at the centre by

If the surface layer is considered as a thin shell, then to a sufficient approximation the volume of the layer is obtained by multiplying the function by the constant height α.

The rate of progress of a substance spreading through this layer will (apart from other variations) follow the rate of change of this volume. Similarly, if the substance is spreading through the body of the egg (with a spherical front of increasing radius), the volume is given by

The rate of change of these two volumes is given in Fig. 3, where the ordinate shows the angle or arc fraction (as in Fig. 1) and the abscissa the respective volume functions. (The absolute scales of the graphs have been adjusted to the same total volume.) It will be noted that the surface volume is symmetrical, i.e. at 0·5 arc fraction, half the volume has been filled while the body volume at that same point is two-thirds complete. Furthermore, both functions have an infinite slope at the beginning.

These functions represent the first analysable component of the observed rate of change. For if the experimental time values are plotted against these functions (Fig. 4) instead of angles or arc fractions, we obtain reduced rates of progress, i.e. plots which have eliminated the fact that the change takes place in or on a sphere. In other words, it is the true rate of spreading of the substance in one dimension or through a cylinder of unit cross-section. This transformation is only valid for ‘equatorial ‘fertilization, when the plane of observation (optical section) is the same as the ‘plane of spreading’, i.e. the plane which passes through the starting-point and the centre of the sphere. When fertilization takes place above or below the plane of observation, the observed angle, θ, of the arc in that plane is not the true angle, ϕ, in the ‘plane of spreading’. They are related to each other as follows, where A is the angle which the two planes make with each other

It will be seen that for θ = 0 (i.e. the beginning of the observation) the true angle already measures A. The difference between θ and ϕ will decrease until they become equal at θ = 90°, i.e. the ‘point of half completion’, where the two planes cross. The observations will end (θ = 180°) before the true change is completed, viz. at ϕ = (180–A) °.

In terms of the time-angle plots this means that the period of observation is shortened both at the beginning and end. If the inclination of the two planes is ascertainable (by measurement of the distance of the fertilization cone to the plane of observation), a transformation of θ to ϕ is possible and equations (2) and (3) could then be applied to the ϕ values. In practice only those film records where sperm entry is near the equatorial plane of observation show the fertilization cone. But deviations of up to 15 ° for A will so be observed, since the depth of focus will record such a structure, although it is about 12 μ above the plane, for an egg of 1oo μ diameter. When measurements on such records are made on the assumption that the observed angle is the true angle, this possible source of error must be taken into account.

Only when the intrinsic rate is uniform will the shortening due to angle A be symmetrical. If, as will be shown later, the intrinsic rate is small at the beginning and increases towards the end of the change, a small angular displacement of the two planes would result in a considerable delay of the first observation, while the error in timing the end-point would be much smaller. The instantaneous rate of change at θ = 90 ° for all fertilizations, in or out of the plane of observation, is, however, also the true rate. The value of this fact is, however, restricted, owing to the very great indeterminancy of readings in that region.

Before analysing the observations in this way, it is useful to consider a number of types of spreading that appear relevant to the problem. They are (1) diffusion, (2) capillary flow, (3) autocatalysis.

1. There are many solutions of the diffusion equation, according to the boundary conditions assumed, such as instantaneous finite sources or continuous supply of diffusing substance or again diffusion into and out of finite or infinite volumes. There is, however, one aspect of all solutions of the equation which is important for our consideration. This is given by Fig. 5. This shows the type of curve which the progress of a given concentration of solute shows with time, (a) the rate of spreading is greatest at the beginning, (b) If the time for the arrival of a given concentration at a given distance L is T, then the time, ⁠, of arrival at half the distance, ⁠, is smaller than half the total time: ⁠.

   Fig. 5.

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   Fig. 5.

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2. In capillary flow through a constant cross-section the rate is only a function of the interfacial tension of liquid and capillary (unless we are dealing with a variable system such as hydrostatistically determined flow). The rate of spreading is shown in Fig. 6. (a) The slope will be constant throughout and its value will depend on the particular conditions of the system. (6) The time of half completion is half the time for the total length ⁠.

   Fig. 6.

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   Fig. 6.

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3. If the substance is produced autocatalytically in the system, the rate of progress will depend again on a number of factors, such as whether the diffusion constants of the reacting and reacted species are the same or different. Further-more, the relation of the concentration dependence of diffusion and autocatalysis will be important. All such cases, however, will show the general behaviour given in Fig. 7. (a) The rate is smallest at the beginning, (b₁) The time of half completion is greater than half the time for the total length or, (b₂). If the initial amount of catalyst is such that the system is nearing equilibrium at L, may be smaller than ’, but in that case the inflexion point will be between t = 0 and ⁠.

The precise form of the equation will be rather complex, being a diffusion equation with autocatalysis as boundary conditions, the possibility of a shape factor entering as well. But the general characteristics will be those described.

On comparing these three models with the experimental evidence in the ‘reduced ‘plots of Fig. 4, it is clear that diffusion cannot be the relevant process. The slope is not maximal at the beginning and ⁠. This is also evident from the curves given by Rothschild (1949, figs. 1 and 2). All the theoretical curves have and all the experimental curves ⁠. This is a far more sensitive test of agreement than the general shape which, from the evidence of Fig. 3, will always be sigmoid.

Capillary flow (an unlikely mechanism in any case) does not agree in its slope and time sequence either. The rate of progress of the observed ‘unreduced ‘change would correspond to the curves in Fig. 3 as these represent also the filling of the respective volumes by a constant supply. It is clear that either the initial slope or the half-time or both do not correspond to the experimental curve (Fig. 2).

Some process involving autocatalysis, on the other hand, appears to fit the experimental data best. The uncertainties in the data make it unprofitable to attempt the evaluation of an equation. For the same reason it is not possible to decide between the alternatives of surface and body spreading.

There is another phenomenon which seems to stand in a relatively simple relationship to the cortical change. This is the elevation of the fertilization membrane which takes place shortly after the cortical change. About the time of completion of this change, the membrane begins to separate from the egg at the place where the cortical change started. It is visible as a crescent standing out from the body of the egg attached at two more or less defined positions. These positions move along the surface of the egg until the membrane has completely separated, ending at the end-point of the cortical change. The progress of elevation can be followed in the same way as the observations on the cortex. If the rate of progress is compared with the cortical change of the same egg a remarkable similarity in the two sequential processes is evident. Figs. 8 and 9 show these two changes in two eggs. The beginning of the membrane change has been advanced for ease of comparison so that it appears superimposed on the cortical change, although they occur one after the other. A number of film records have been so analysed, and in each case the agreement is unmistakable. Furthermore, this is so whether fertilization was equatorial or not. In the egg from which Fig. 9 was obtained no fertilization cone was visible and the total time was, as expected, significantly shorter than for the egg of Fig. 8. Yet the curve for the lifting of the membrane runs parallel with that for the cortical change.

An interpretation of this correlation can be given as follows. If the observed cortical change is a precursor of a series of reactions resulting in the elevation of the membrane, then the cortical reaction must be the rate-determining step, i.e. it is slower than all other processes.

Alternatively, the lifting of the membrane may be the physical consequence of the completion of the cortical reaction. The observed optical change may be the first signs of a single condensation or polymerization process which results in the production of material which unites with the vitelline membrane.

In any case, the close correlation of the two observable phenomena strengthens the reality of the time sequence, and makes it possible to measure the ‘same reaction’ by two observationally independent methods.

We shall now consider whether any of the other work which has been carried out on the reaction of echinoderm eggs to fertilization and particularly that involving artificial activation, provides data compatible with an autocatalytic mechanism or will enable us to-decide between the alternatives of the cortical or cytoplasmic routes for its transmission. There are no strictly comparable reports for Psammechinus. However, Moser (1939a), studying Arbacia punctulata, observed a wave of roughening spreading over the surface of the egg from the point of sperm entry, followed, shortly after the completion of the change, by the elevation of the membrane starting from the same point. The roughening appears to be due to the breakdown of granules lying immediately beneath the cortex. The structural nature of the change is thus different from that observed by Rothschild & Swann in Psammechinus, where the increase in light scattering is probably due to the formation of a more granular structure. However, while the optical concomitants of the change will depend on the state of aggregation of the layer, which may be different in the two genera, the underlying chemical basis of the change may well be the same. In view of the identity of the response sequence of the two processes in the two genera, we suggest that we are concerned with the same intrinsic phenomena. It is worth pointing out that Moser’s theory that membrane formation depends on a vacuolization consequent on the breakdown of granules is difficult to accept unless one makes the assumption that the membrane is produced in two different ways in Arbacia and Psammechinus. There are no quantitative data for the kinetics of the change, but Moser gives an average value of 9·9 sec. from fifty-seven measurements. For reasons discussed by Rothschild & Swann in their paper, the longest and not the average time would be nearer the true response time. Here again, however, differences in temperature, size, viscosity and state of aggregation from one form to another could result in absolute differences without implying a difference in the intrinsic nature of the response.

Moser (1939b, 1940) studied a considerable number of agents (saponin, toluol, urea, thiourea, glycerine, sucrose, mechanical puncture, ultraviolet and direct current) which can act as artificial activators and produce the cortical response followed by the elevation of the membrane. On the autocatalytic hypothesis one might expect initiation to be caused by the introduction of some of the catalyst. These observations show that the initiation of the cortical response cannot be entirely dependent on the spermatozoon bringing in a quantity of catalyst. One must suppose that the action of the spermatozoon or of the artificial activators either enables a catalyst to enter from the sea water, or initiates the release of a catalyst already contained in an inactive form in the egg. The evidence that the response is inhibited by the removal of calcium ions from the water and, according to Moser (1939b), ‘presumably from the cortex’, might suggest that the calcium ions are the actual initiators, but it is equally possible to suppose that they are concerned not with the initiation but with the capacity to carry out the response. We shall return to this aspect later. There is then nothing in these observations incompatible with the suggestion that a catalytic agent is released from within the egg itself. In fact, the occurrence of artificial activation might be expected on our hypothesis since the mechanism does not require the intervention of any specific agent.

It is also not unexpected to find that when an activating agent (urea solution) is allowed to flow from one side into the drop containing the egg, the cortical change, followed by the membrane, proceeds from this side in a wave-like manner, while if the eggs are placed in a solution (e.g. saponin) so that there is no preferential direction of exposure, the response occurs more or less simultaneously over the whole surface. From our point of view a more important observation is that of Kitching & Moser (1940), who found that absence of oxygen does not prevent or even slow down, the cortical change or the membrane elevation, although it inhibits cleavage. Furthermore, the time relations of the cortical change and membrane elevation, initiated by saponin, urea, sucrose and puncture, were the same with or without oxygen. This rather strongly suggests the autocatalytic break-down of a metastable system which, once it has started, would be self-perpetuating and would be independent of the free energy supply of the respiratory system.

When Arbacia eggs are strongly centrifuged the cortical layer of granules will remain in position even when the inner cytoplasm is stratified. Such eggs do not lose the ability to exhibit the cortical reaction and membrane elevation, but the time-relations between these two processes are frequently altered. Thus Moser (1939a) has shown that following fertilization at the centrifugal pole, membrane elevation begins when the cortical reaction has reached half completion, although in uncentrifuged eggs (as in Psammechinus) this reaction is complete before the elevation begins. He reports (1939b), precisely the same relations when initiation is effected by saponin applied at the centrifugal end. He further found that while centrifuged eggs can apparently be stimulated by spermatozoa at any point on the surface, saponin can initiate the response only at the centrifugal and puncture only at the centripetal end. These facts suggest that different parts of the egg may have different thresholds or quantitatively different initiation responses at least with respect to certain activating agents. At any rate the evidence clearly indicates that the condition of the internal cytoplasm has a considerable effect on the progress of the cortical reaction. In view of this it would be difficult to suppose that the processes which bring about the spreading of the cortical reaction involve that layer only. It might still be, however, that the change is transmitted primarily within that layer but involves the mobilization into it of catalyst released at the place of initiation from the underlying cytoplasm, or of substances necessary for propagation, this mobilization being influenced by the stratification of the cytoplasm in centrifuged eggs.

Motomura (1934, 1941) has described a cortical layer in Strongylocentrotus pulcherrimus, which he considers comparable to Moser’s granular layer. He describes the discharge of the granules from the cortical zone on to the membrane following fertilization, or activation with butyric acid or urea. This discharge is a very slow process, taking as long as 10 min. It seems to be concerned mainly with the hardening of the fertilization membrane and not with its initial elevation. He does not describe any cortical reaction which preceded the elevation of the membrane, and it is possible that in this form the reaction, if it occurs, is un-accompanied by any optical change. The process described by Motomura is therefore not comparable to the reactions we have been discussing, and does not provide any reason to doubt the hypothesis which has been advanced.

In a recent publication (Allen, 1954) experiments on fertilization of Psammechinus miliaris eggs, drawn into capillaries of various diameters, are reported. It was possible to follow the cortical granule transformation, subsequent to fertilization at one end, along the cylindrical portion of the egg. In view of the constriction in the tube the elevation of the membrane did not take place (except at the end or ends), although it could be shown in some cases that the membrane had separated by the possibility of sliding the eggs back and forth in the membrane.

As in the present report, the wave of propagation had no sharp front but showed a region (20–30μ) in which the granules were breaking down at random. They were smaller and became less plentiful towards the portion already changed. In dark ground a yellow colour is replaced in a wave-like manner by a brilliant white. Here, too, the intermediate region showed patches of yellow.

In twenty-nine cases the cortical change proceded to completion to the far end of the egg, but in fifty-six cases (the figure 63 is mentioned in the text) the change apparently ‘died out at some point on the cylindrical surface’. The rate of change of cortical transformation was measured in ten of the eggs by noting the time that single granules broke down first ‘at known distances from the point of sperm entrance’. Zero time was assumed as the time when the surface of the spherical portion of the front end began to roughen, ‘evidently caused by the breakdown of cortical granules’. Only three representative curves are given and these are reproduced in Fig. 10. The ordinate does not show the observed distances but area of response covered (calculated, from the distances and the value of 97μ for the diameter of the spherical egg, on somewhat inaccurate assumptions). This representation is similar to that given by the V_s curve in Fig. 4 although it would have been more useful for comparison purposes to express these as fractions of total surface instead of absolute μ².

The main points to note are the greatly extended time and the shape of the curves. Curves c and d clearly correspond to diffusion curves (cf. Fig. 5). In the absence of the present analysis this might have been considered powerful support for Rothschild’s hypothesis. Curiously enough Allen considers these as evidence against it, asking why, since there has been no change in either cortical or cytoplasmic volumes, these ‘should still not be filled by the amount of diffusing substance introduced by one, or even two, spermatozoans’.

The answer is as follows. The evidence presented does not show that the volume is not being filled but that the rate at which it is being filled decreases with the increase in distance. Now the rate is, of course, a function of the geometry of the egg. Allen considers ‘stretching, straightening of the egg surface and contact with the glass: three inseparable variables’ as the only factors that have been changed, while of course the diffusion paths, both cortical and cytoplasmic, have been increased and the cross-sectional areas decreased. The time scale of diffusion will therefore be ‘stretched’ considerably.

Allen offers an explanation of the results by postulating ‘evenly spaced units of some sort’ in the cortex which can exist in ‘non-activated or activated forms’. He then postulates that the spermatozoon initiates a ‘chain reaction’ among the units, a suggestion already hypothecated by Runnstrôm & Kriszat (1952). (It is clear that the term ‘chain reaction’ is not used in its accepted chemical sense.) Both these authors and Allen cite, in support of the hypothesis, the observed acceleration of the wave when it passes over the end portion of decreasing area. It has already been pointed out (Fig. 3) and is also evident from Rothschild’s theoretical curves that, for geometrical reasons, any process travelling over that portion will show acceleration.

To account for the decreasing slope of the curves he postulates ‘that the number of units activated decreases for each successive unit of time’. On the other hand, to account for the cases of ‘complete fertilization’ (over 35 % of the control eggs), when the slope increases, he postulates the opposite, viz. ‘the successful conversion of an increasing proportion of units’. With this somewhat flexible hypothesis, the difference in behaviour between elongated and normal eggs is explained by reference to a ‘disruption’ of ‘the structure in which the units we have postulated play an integral part’ or ‘due to the fact that the postulated units become farther apart’ because of stretching.

The disruption explanation is made unlikely by the fact of ‘continued complete fertilizability of the entire unfertilized part’ and by the fact that the return of stretched eggs to a solution ‘removes the inhibition of membrane formation at the sides in contact with the capillary and, as a rule, at the hind end as well ‘(Horstadius & Runnstrôm, 1953).

The stretching explanation is contradicted by the observation of Runnstrôm & Kriszat (1952) on eggs which became attached to the bottom of a glass dish. The propagation of the impulse was inhibited in that part of the surface which was in contact with glass. This portion is not stretched, if anything, it is compressed. As in the capillary experiments, in a number of cases when such ‘partially fertilized ‘eggs could be detached without injury, normal membrane formation could be induced in that portion.

It is therefore clear that, under the prevailing experimental conditions, the evidence presented shows the propagation of the response to obey not an autocatalytic mechanism but strongly suggests a diffusion process. This apparent contradiction between Alien’s results and those of Rothschild & Swann can be resolved if it is remembered that calcium ions are necessary for the response to take place. Now, apart from the geometrical parameters already discussed, eggs inside capillaries as well as the attached eggs differ from the spherical eggs in solution by having part of their surface not in contact with calcium containing water. The necessary calcium can only be brought to the site of reaction either by diffusion through the egg or through the space between egg and glass.

Runnström & Kriszat report that their jelly-free eggs adhered strongly to the glass which would provide a very good seal. The complete failure of the response in the adhering portion even after prolonged times (up to 120 min.) shows that the calcium does not diffuse through the egg or cortex. Adhesion could be prevented by the addition of o·1−0·2% serum albumin, a procedure adopted throughout Alien’s experiments. Under these conditions diffusion can take place through the thin annular space between the egg and the capillary. It is therefore suggested that the process which was measured in curves c and d of Fig. 10 was the diffusion of calcium ions through the annular space. This interpretation is strengthened by the following facts reported by Allen. The probability of ‘complete fertilization’ decreases (i.e. the number of cases with a very low finally observed rate of transformation increases) as the ‘degree of stretching’ increases (i.e. as the length of the cylindrical portion increases). This is in conformity with expectation since an increase in the diffusion path decreases the rate in the well-known manner. In addition, the greater compression and distortion of the eggs in narrow tubes will cause these to have a tighter fit with consequent decrease in cross-sectional area of the annular space.

A decision as to the alternatives of calcium action, discussed before, may now be made. The calcium ions cannot be merely the initiators but are necessary for the carrying out of the response. Furthermore, they cannot be present to any appreciable extent in the cortex and are not liberated in the process of activation as suggested by Moser (1939a). They must be available at any portion of the surface where the reaction takes place. We can formally represent the situation by the following bimolecular reaction scheme, where M represents the component in the surface undergoing transformation.

Or

In the presence of excess of calcium the reaction proceeds as a first-order autocatalytic process. When calcium is limited the rate will depend on its concentration which, in the capillary experiments, is limited by diffusion. This is then the rate-determining step. In the absence of calcium no reaction takes place.

Curve b in Fig. 10 represents an intermediate case. This was a moderately elongated egg (188μ) and consequently has only a portion. (<2/3) of its surface obstructed. Although the vital information about the initial slope is missing, and it is impossible to say whether fertilization was equatorial or not, the change of slope is significant. While in the middle portion the rate is decreasing with diffusion as determinant, as the wave approaches the free end and reaches the region of unlimited calcium supply the autocatalytic mechanism takes over.

Some indications as to the nature of the change, as distinct from its propagation mechanism, emerge from this analysis. Since calcium enters the egg at all points along the response region and only when the response reaches any point, an increase in permeability of the surface must be involved. One might tentatively suggest that it is this change in permeability which constitutes the primary process of activation. Spermatozoa or any of the artificial agents can then be considered to effect an increase in permeability at the site of action which allows calcium to enter and convert the surrounding surface components into more permeable products. The initial increase in permeability is a sufficiently unspecific event to be caused by a large variety of agents which, with a surface of complex constitution, could effect the change by a variety of mechanisms. Whether the change is temporary or permanent is difficult to say since other processes such as membrane elevation and hardening supervene after a short time. The cortical granule transformation would then be considered synchronous with or immediately following the primary change. (See discussion by Sugiyama, 1953.) If the ‘dying out’ of the response in the region of low calcium concentration were a genuine ‘death’, i.e. that after an appropriate time interval the re-supply of calcium to the site would not result in a regeneration of the response, then the temporary nature of the response would be established. The published evidence by Allen points to this but does not permit a decision between it and the alternative of closure by a secondary process to be made. It is possible that this change plays a part in the block to polyspermy.

There is considerable information both on permeability and the role of calcium in activation and subsequent processes, but since most of it refers to experimental conditions very different from those considered, it would be inappropriate to discuss these here. However, it is worth pointing out that the eggs of some marine invertebrates have been shown to exhibit no measurable increase in permeability to water at fertilization. This is not incompatible with the mechanism suggested here. Firstly, there is abundant evidence from tracer work that transport across membranes, both active and passive, can be highly specific. It is clear that the conditions for permeability to positively charged calcium ions would be very different from those for neutral water molecules. Secondly, the change may be of short duration, sufficient for the passage of catalytic quantities of calcium, but not long enough for significant amounts of water to be detected by the methods employed.

Some of the results of Sugiyama (1953) possibly raise another aspect. Eggs of Strongylocentrotus pulcherrimus, pressed between cover-slip and slide into the shape of disks, were exposed to solutions of various activating agents for a short time. Sugiyama divides these agents into two classes, those having a ‘propagating nature’ and those having a ‘non-propagating nature’. With the former the cortical granule breakdown, initiated in the exposed equatorial region, continues over the whole surface, with the latter it is confined to the exposed region. He suggests that the non-propagating agents affect the granules directly without initiating the (invisible) ‘fertilization wave’. As no rate date are available, it is impossible to say whether there are real differences between agents or whether it is merely a time-scale difference. Allen (1954, p. 422) in similar partial exposure experiments on elongated Psarnmechinus eggs also describes a class of non-propagating agents but finds that others produce a wave-like breakdown which is slower than the normal fertilization response. Only one of the agents used (periodate) appears to initiate a response identical with that initiated by spermatozoa—if anything it is more effective. There is therefore a suggestion of a gradation of effects as an alternative to the idea of different mechanisms.

Differences in initial rate and total time between one experiment and another or between different activating agents could be caused by differences in the intensity and extent of the initial permeability change which is a function of the agent as well as the egg. In an autocatalytic equation the initial amount of catalyst as well as the specific rate constants determine the kinetics of the process. The state of maturity of the egg and its treatment before fertilization would influence mainly the internal specific parameters, while the nature and concentration of the activating agent or the age of the spermatozoon would influence mainly the initial parameters of the system. Species specific differences must be added to this. In view of this and the paucity of consistent experimental information on the nature of the substances involved it would be unfruitful to discuss these changes on the molecular level.

The kinetics of the dark ground cortical change in fertilized sea urchins has been analysed. In normal eggs of Psammechinus miliaris the change appears to obey an autocatalytic mechanism.

The evidence from artificial activation suggests that the initiation of the response is caused by a relatively unspecific event.

The critical role of calcium is considered in relation to the evidence from eggs fertilized in capillary tubes. This suggests that calcium ions are not concerned with the initiation but with the propagation of the response.

The primary change in activation may consist of an increase in permeability at the site of initiation.

My thanks are due to Lord Rothschild, F.R.S., Prof. M. M. Swann and Prof. C. H. Waddington, F.R.S. for helpful discussion and criticism; and to the Nuffield Foundation for a grant.