DEVELOPMENTAL

BIOLOGY

i?&327-341

Voltage Response

(1979)

to Fertilization and Polyspermy and Oocytes LOUIS J. DEFELICE’

in Sea Urchin Eggs

AND BRIAN DALE

Stazione Zoologica, Naples, Italy Received August 7, 1978; accepted in revised form March 30, 1979 collision rates of sperm with eggs and oocytes of the sea urchins Psammechinus and Paracentrotus lividus have been studied using an electrophysiological method. A monospermic response in eggs consists of a l- to 2-mV step depolarization of the egg plasma membrane accompanied by an increase in voltage noise. The step precedes the main positive-going depolarization by approximately 13 set at room temperature. If other successful collisions occur during this 13-set period (indicated by additional steps), the egg is polyspermic. It is shown by direct observation that each step depolarization signifies the entry of a single sperm. No evidence for an electrically mediated fast block was found. The average rate of successful sperm-egg encounters increases with sperm density, although individual steps appear to occur randomly. Step depolarizations also occur in oocytes, however, they usually decay after several seconds and are not followed by a large, positive-going depolarization. The rate of occurrence of such steps increases with sperm density over the range lo5 to 10’ sperm/ml. The original evidence of Rothschild and Swann for a fast partial block is compared with a model of polyspermy suggested by our experiments. Reasonable agreement between our method of counting successful collisions (in oocytes and eggs) and the method used by Rothschild and Swann (for eggs) was obtained for sperm densities below 106/ml. The results diverge for higher sperm densities, our method giving higher values. A test for the hypothesis of a fast partial block to polyspermy is suggested, using our method of counting successful sperm-egg collisions. Successful

microtuberculatus

INTRODUCTION

To preserve the diploid state of eukaryotic organisms it is essential that only one sperm nucleus fuses with the egg nucleus. In a minority group of animals, reptiles, birds, sharks, and salamanders, several sperm may enter the egg but only one fuses with the egg nucleus. The supernumerary sperm degenerate and do not interfere with development (Rothschild, 1954). In other animals, for example, echinoderms, the entry of more than one sperm results in abnormal cleavage. Under laboratory conditions, however, the incidence of abnormal cleavage due to polyspermy is low even at relatively high sperm densities. This observation led to the suggestion that in such animals a mechanism existed at the ’ Permanent Emory University,

address: Department Atlanta, Georgia

of Anatomy, 30322.

egg surface which excluded supernumerary sperm. Sea urchins have been used extensively to study this mechanism. There appears to be general agreement on a slow permanent block to polyspermy in sea urchin eggs. In Psammechinus, no sperm can enter the egg after a mean time of 63 set at 16°C following the interaction of the fertilizing spermatozoon (Rothschild and Swann, 1952). This permanent block corresponds to the completion of the cortical reaction and has been attributed to the formation of the hyaline layer (Hagstrom and Hagstrom, 1954; Lonning, 1967a) and to the release of proteases from the cortical granules (see Epel (1978) for a review). In addition to this slow permanent block, Rothschild and Swann (1952) suggested that a faster partial block may exist in sea urchins. This would consist of a rapid 0012-1606/79/100327-15$02.00/O Copyright 0 1979 by Academic Press, Inc. All rights of reproduction in any form reserved.

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change of the egg surface, shortly after the successful interaction of the fertilizing spermatozoon, causing a decrease in sperm receptivity. The probability of a second successful sperm egg collision would then be reduced. The concept of a fast block has been supported by some workers (Presley and Baker, 1970; Jaffe, 1976) and refuted by others (Hagstrom and Allen, 1956; HagStrom, 1956a; Byrd and Collins, 1975). The assumption that the fertilization reaction may be treated as a first-order chemical reaction has also been criticized (Hultin and Hagstrom, 1956) and a new model put forward (H&in, 1956). Rothschild and Swann (1952), Hagstrom and Allen (1956), Presley and Baker (1970), and Byrd and Collins (1975) measured rates of successful sperm-egg collision indirectly by counting the percentage of fertilized eggs at different times following insemination. The last three studies also counted the actual number of sperm nuclei which entered the eggs. Jaffe (1976) suggests that the fast block to polyspermy in sea urchins is electrical; the fertilizing spermatozoon causes a rapid change in potential of the egg plasma membrane, preventing other sperm from interacting with it. Only one-third of the eggs studied by Jaffe exhibited such a rapid change in potential. We report here a direct method for monitoring successful sperm-egg collisions as they occur in time in an individual egg. The method is based on the observation that a successful collision of a spermatozoon results in a step depolarization and an increase in noise across the egg plasma membrane. MATERIALS

AND

METHODS

Experiments were carried out on Psammechinus microtubereulatus and Paracentrotus lividus collected from the Bay of Naples between December and April and in October. Eggs and sperm were obtained

VOLUME 72.1979

directly from the gonads by dissection. Oocytes were identified by the presence of a germinal vesicle. Jelly coats were removed by exposing eggs to acidified seawater at pH 5.5 for 2 min. Intracellular electrical recordings were obtained from eggs kept in natural seawater at 18-22°C using 3 M KC1 or 1.8 M Kcitrate microelectrodes of 30- to 50-Ma dc resistance. Citrate electrodes were used when it was necessary to follow cleavage; eggs impaled with KC1 electrodes appeared to cleave less reliably than eggs impaled with K-citrate electrodes. An impaled egg (or oocyte) kept in a shallow bath was exposed to seawater containing a known concentration of sperm by applying a drop directly above the egg. Dense white sperm was taken up in a Pasteur pipet from fresh testes and was gently diluted with seawater. A control drop was placed in a hemocytometer to determine sperm concentration. The tip of the pipet was placed just above the impaled egg and one or two drops were released carefully, not to disturb the impalement. The impaled egg and surrounding eggs were completely enveloped by the droplet viewed under the microscope. We were recording continuously on magnetic tape; all data correlated with sperm concentration refer to the first electrophysiological events that occur and to the concentration in the applied drop. This method of sperm addition prevents rapid mixing in the bathing medium; nevertheless, some of the variation in our data could be due to the gradual dilution of sperm as they spread throughout the dish. This sort of error is difficult to quantify; the voltage responses began immediately after application of the sperm droplet, and at least we have an upper limit on the concentration that should be used in the correlation. Our method allowed the application of sperm within 2 min of its extraction from the testes. Time was considered the most important factor in delivery because of the rapid decline of sperm fertiliz-

DEFELICE

AND DALE

Voltage Response to Fertilization

ability. (See the discussion near Fig. 4.) The electrical recordings were made at low gain (25~) with dc-coupled amplifiers to record the steps and the fertilization potentials, and at high gain (300x) with accoupled amplifiers (0.015 Hz) to record electrical noise during the steps. Signals were stored on FM tape at 3.75 ips (dc, 625 Hz) for subsequent analysis. All of the records shown are from tapes; l-Hz ac coupling was used for the photographs of noise traces. Polyspermy in eggs was determined by two methods: (1) by observation of first cleavage-monospermic eggs divide into two equal cells, whereas polyspermic eggs cleave abnormally, producing three or more cells at once; (2) by counting the number of sperm nuclei in the experimental egg, following the method of Byrd and Collins (1975). RESULTS

The resting potential of mature eggs of and Paracentrotus in nat-

Psammechinus

329

ural seawater varies from -8 to -16 mV. When sperm at a density of 107/ml are added to the external medium, the resting potential undergoes a transient change to approximately +20 mV. The membrane repolarizes gradually to its rest value and ultimately to potentials near -60 mV. This response has been reported for other species of sea urchin and has been called the fertilization action potential (Steinhardt et al., 1971) or simply the fertilization potential. At high sperm densities, the depolarization is composed of two phases; the initial phase has been called the shoulder of the fertilization potential (Ito and Yoshioka, 1973). Figures la and b show that the leading edge of the shoulder is composed of discrete events; in this case, there are three sharp steps which then merge into the shoulder. The lower trace of Fig. lb shows membrane noise during the leading edge of the shoulder. The three transients in the lower, accoupled trace correspond to the three steps

FIG. 1. Intracellular recordings from eggs of Psammechinus microtuberculatus kept in natural seawater at 22°C. (a) The fertilization potential of an egg inseminated with 10’ sperm/ml. Zero potential is indicated by a dash preceding the fertilization potential. The horizontal bar represents 5 set; the vertical bar represents 10 mV. (b) The upper trace is an amplification of the leading edge of the shoulder of (a). The lower trace shows the noise during the same period. The horizontal bar represents 1 set; the vertical bar represents 1 mV for the upper trace and 0.4 mV for the lower trace. (c) The fertilization potential of an egg inseminated with 10” sperm/ ml. Zero potential is indicated by a dash. The horizontal bar represents 5 set; the vertical bar represents 10 mV. (d) The upper trace shows the step amplified; the lower trace shows the increase in noise accompanying a step. The horizontal bar represents 1 set; the vertical bar represents 1 mV for the upper trace and 0.4 mV for the lower trace.

330

DEVELOPMENTAL

BIOLOGY

in the upper, dc-coupled trace. There is an increase in the membrane voltage noise at each step. (The voltage noise increase in the first, second, and third steps has been studied using two recording electrodes. A preliminary report has appeared (DeFelice and Dale, 1979) and a full-length paper is in progress.) At sperm densities of 105/ml or lower, the entire shoulder region is composed of a single step (Figs. lc and d). Whether composed of many events or a single step, the shoulder lasts for approximately 13 set at 22°C. Figure Id shows the step in greater detail. A single step has an amplitude of l2 mV and is always accompanied by an increase in noise. An interpretation of this noise increase has been made (Dale et al., 1978). At sperm densities below 105/ml, it is not

VOLUME

72,1979

uncommon to wait several minutes for a reaction to occur. A single step is the minimum detectable event during the shoulder phase of the fertilization action potential. The egg that displayed the response shown in Fig. Id cleaved normally. We conclude that a single step and simultaneous noise increase correspond to the successful interaction of the fertilizing spermatozoon. By this argument, several steps would indicate several successful interactions, and therefore an egg displaying a multistep shoulder should be polyspermic. The egg that displayed the response shown in Fig. lb cleaved abnormally. Figure 2 shows the effect of sperm density on the configuration of the shoulder region for eggs that cleave abnormally. At sperm densities greater than 10’ sperm/ml, exemplified by Fig. 2a, it is difficult to iden-

FIG. 2. Intracellular recordings from eggs of Psammechinus (b and c) and Paracentrotus (a and d) showing the variation in configuration of the shoulder region with sperm density. The upper trace in each quadrant is dc coupled, the lower trace (ac coupled at 1 Hz) shows the membrane noise. Sperm density was greater than IO8 sperm/ml in (a), approximately 5 x 10’ sperm/ml in (b), and approximately 5 x 10” sperm/ml in (c) and (d). The horizontal bar represents 1 set for all traces. The vertical bar represents 1 mV for all dc-coupled traces and 0.4 mV for all ac-coupled traces.

DEFELICE

AND

DALE

Voltage Response to Fertilization

tify single steps on the dc trace, however, the gradual depolarization and increase of noise are consistent with a summation of closely occurring events. At sperm densities between lo* and lo7 sperm/ml, exemplified by Fig. 2b, discrete events occur on the leading edge of the shoulder. Each step is accompanied by an increase in noise; the steps gradually merge to form an apparently continuous phase of the shoulder region. Figure 2c and d are the result of insemination at sperm densities between lo7 and lo6 sperm/ml. Figure 2c shows three distinct steps and Fig. 2d shows two distinct steps. All four eggs in Fig. 2 cleaved abnormally. The steps and accompanying noise increases occur in both Paracentrotus (Figs. 2a and d) and Psammechinus (Figs. 2b and c). We have also studied this phenomenon in Arbacia, where we obtain traces qualitatively similar to the samples shown in Fig. 2. In a separate series of experiments, the experimental egg was fixed and the number of sperm nuclei in the egg was determined under phase microscopy (Byrd and Collins, 1975). Figure 3a shows the result of one such experiment. Three distinct sperm nuclei are visible in the micrograph (indicated by arrows); two others are also seen out of focus. Altogether, nine nuclei were found in this egg. The transmembrane voltage which accompanied the fertilization of this egg is shown at three magnifications. The fertilization potential is seen in Fig. 3b; details of the shoulder region are shown at higher magnification in Fig. 3c. Four or five steps are evident at the beginning of the shoulder. Some steps may be present in the depolarization phase following the shoulder, though this is less certain. The lower trace in Fig. 3c shows the noise increase that accompanies the steps. Table 1 summarizes our results from seven experiments. The number of steps in the shoulder and the number of sperm nuclei found in the egg are well correlated, indicating that each step depolarization signifies a successful sperm-egg interaction.

331

Table 1 also shows that the number of sperm which enter an egg increases with sperm density. The effect of impalement on polyspermy can be assessedby comparing the number of steps in the experimental egg with the percentage of abnormal cleavage in the surrounding eggs. The results from 18 such experiments are shown in Table 2. If the impaled egg showed a single step during the shoulder phase of the fertilization potential, the majority of the surrounding eggs cleaved normally. If the impaled egg showed several steps, the majority of surrounding eggs cleaved abnormally (one exception was found in Experiment 3). In Naples, polyspermy in sea urchins is more frequently encountered in the period December-April than July-October (HagStrom, personal communication). The experiments shown in Tables 1 and 2 were done during October. Successful collisions appear to occur randomly, with no preference for long or short latencies between steps. Compare, for example, Fig. lb and Fig. 2c. In Fig. lb, the interval between the first and the second step is about 1 set and the interval between the second and the third step is about 0.2 sec. In Fig. 2c, the reverse is true. Although a statistical analysis has not been done, the examples shown in Fig. 2 are representative. The effect of sperm density on the average rate of successful collisions can be measured by comparing the number of steps which occur during the shoulder with the density of sperm used for insemination. At higher sperm densities, where many steps occur, successive steps eventually become indistinct (Fig. 2). In such cases,steps can only be counted accurately at the beginning of shoulders at medium sperm densities and not at all at higher densities. At low sperm densities, the onset of the main depolarization wave after the shoulder makes it impossible to count steps below one per 13 set at room temperature. For these reasons, we have used oocytes to

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VOLUME 72,1979

FIG. 3. (a) Phase-contrast micrograph of a Psammechinus egg inseminated at 3.5 x lo7 sperm/ml (Table 1, Expt 1). Three sperm nuclei are indicated by the arrows; altogether, nine sperm were found in this egg. The egg diameter is about 100 pm. (b) The fertilization potential that accompanied the insemination shown in (a). The vertical bar represents 10 mV; the horizontal bar represents 5 sec. The horizontal bar also indicates the level of zero potential. (c) The shoulder of the fertilization potential at higher magnification. The upper trace is dc coupled (vertical bar, 1 mV). The lower trace is ac coupled at 1 Hz (vertical bar, 0.4 mV). Four or five step depolarizations are seen. The horizontal bar represents 1 set for both traces.

study successful collision rates over a wide range of sperm density. The germinal vesicle stage oocyte is the last stage in the maturation of the sea urchin egg prior to polar body ejection. These oocytes are the same size as mature eggs but have no cortical granules and are incapable of the cortical reaction (Lonning,

1967b). Such oocytes have resting membrane potentials in the range -50 to -70 mV. Following insemination, step-like depolarizations occur; each step is accompanied by an increase in noise. These steps are similar to those seen in mature eggs except they are generally larger and tend to decay after a few seconds (see inset in Fig.

DEFELICE

Voltage

AND DALE

1

CORRELATION BETWEEN THE NUMBER OF DECONDENSED SPERM NUCLEI IN EXPERIMENTAL EGG AND THE NUMBER OF STEPS IN THE TRANSMEMBRANE ELECTRICAL RESPONSE TO FERTILIZATION” Expt

1

2

3 4 5 6 7

No. of steps in shoulder

4 definite merging der 5 definite merging der 4 definite 2 definite 3 definite 2 definite, steps 1 step

No. of sperm nuclei located in egg

Sperm concentration per ml

steps, then into shoul-

9

3.5 x IO’

steps, then into shoul-

7

3.5 x lo7

steps steps steps 2 indefinite

4 2 3 4

6.2 6.2 6.2 3.5

1

6.2 x lo”

x x x x

10” 10” lo6 10”

n Experiment

1 is shown

in Fig. 3.

CORRELATION

BETWEEN

POLYSPERMY IN EGGS SURROUNDING THE IMPALED AND THE NUMBER OF STEPS IN THE SHOULDER

TABLE

Expt

No. of steps

in shoulder

No distinct No distinct No distinct 5 steps, then No distinct No distinct No distinct 4 steps, then 5 steps, then 5 steps, then 2 steps 3 steps 1 step 1 step 1 step 1 step 1 step 1 step

steps steps steps shoulder steps steps steps shoulder shoulder shoulder

2

Cleavage Polyspermic

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

11 9 7 8 16 10 6 10 37 28 21 4 4 0 4 6 0 3

333

to Fertilization

possible in mature eggs. Each step signifies a successful sperm-egg collision since the number of steps correlates with the number of blebs visible on the oocyte surface. The number of blebs was counted by focusing back and forth through the diameter of the impaled egg during the first 5 min following the recording. In three cases, where the frequency of steps was low (less than 8 in 16 set), the total number of steps and the number of blebs observed agreed perfectly. The inset in Fig. 4 is an example of the response of a germinal vesicle stage oocyte to insemination at a sperm density of 3.5 x 107. Eight steps occur in 16 sec. From such records we have calculated the successful collision rate for sperm densities between lo5 and log/ml; these are shown as solid points in Fig. 4. The successful collision rate increases monotonically with the sperm density. In mature eggs, for densities between 5 x lo5 and lo7 sperm/ml, successful collision rates agree with those obtained for immature eggs. (See the discussion near Fig. 4.) The successful collision rate depends on

4). Their larger size facilitates counting at higher sperm densities. Because there is no block to polyspermy in immature eggs, sperm continue to enter for several minutes, thus, the rate of occurrence of steps can be measured at frequencies well below those TABLE

Response

in surrounding Monospermic 5 8 11 5 11 6 4 4 6 16 3 10 55 13 12 21 12 12

EGG (JUDGED eggs

BY CLEAVAGE) Sperm concentration per ml

Uncleaved 6 3 0 3 1 5 1 4 7 1 6 4 4 1 4 0 4 3

2.4 2.1 2.4 2.4 2.1 2.1 2.1 5.7 5.2 5.2 2.4 2.4 2.4 5.3 5.3 5.3 2.4 2.4

x x x x x x x x x x x x x x x x x x

lo” loy 10” 10” 10” loa lo8 10; 10’ 10’ 10’ 10” 10” lo” lo” lo” 10” lo”

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VOLUME 72,1979

FIG. 4. The number of spermatozoa that collide per unit time (vertical axis) as a function of the sperm density (horizontal axis). The inset shows a typical response to insemination of a germinal vesicle stage oocyte. Each step (upper trace) and each noise increase (lower trace) represent a successful sperm collision. The horizontal bar represents 2 set; the vertical bar represents 10 mV for the upper trace and 1 mV for the lower trace. From such records the number of steps/set was measured. These are plotted as the solid points; the number of steps is indicated by each point. Experiments from three different batches of eggs are indicated by the filed squares, triangles, and circles. The points (Y and o’ are successful collision rates for mature eggs determined by Rothschild and Swann (1951,1952). The line Zrepresents the theoretical collision rate (successful and unsuccessful) of sperm with eggs originally postulated by Rothschild and Swann (1949). See text for details.

the length of time that sperm have been in the diluted condition. In all our experiments, sperm were kept in the gonads (or in the dense state that seepsfrom dissected gonads) until the egg or the oocyte was impaled. The sperm was then diluted to the appropriate density and applied immediately to the bath. If sperm were applied 10 min after dilution, collision rates were approximately one-tenth those shown in Fig. 4. The line labeled 2 in Fig. 4 is the theoretical collision rate (all collisions, successful or not) of sperm and eggs described by

the equation 2 = (a&)n, where a is the egg radius (taken as 50 pm), F is the mean speed of the spermatozoon, and n is the sperm density (Rothschild and Swann, 1949). This line is based on an idealized model of sperm-egg encounters and represents an upper limit on the mean collision rates one expects. The groups of points (Yand (Y’are successful collision rates determined indirectly by kinetic experiments (Rothschild and Swann, 1951, 1952) for mature Psammechinus miliaris eggs

DEFELICEANDDALE

Voltage Response to Fertilization

and shall be compared with our results in the Discussion. DISCUSSION

We have shown that a successful spermegg collision results in a l- to 2-mV step depolarization and a noise increase across the egg plasma membrane. The membrane remains in this state for 13 set at 22°C and then begins a slow positive-going depolarization. If we increase the probability of a second successful collision by increasing the sperm density, another step similar to the first may occur in the 13-set interval. Each step indicates a sperm entry, and the number of sperm which enter an egg increases with the sperm density. This is in agreement with the results of Byrd and Collins (1975), who have shown in Strongylocentrotus that the number of sperm nuclei per egg increases as a function of the spermegg ratio. They conclude that there is no change in egg receptivity for at least 12 set after the first spermatozoon-egg fusion. Our experiments, and those of Byrd and Collins, argue against the hypothesis that there is a fast block to polyspermy. A mechanism for a fast partial block to polyspermy has been proposed by Jaffe (1976). Following insemination of Strongylocentrotus, egg membrane potentials changed in less than 3 set from the resting level of -56 to -79 mV to a plateau of -35 to +23 mV. All eggs which went positive were monospermic (8 cases), whereas eggs with a negative plateau were either monospermic (6 cases) or polyspermic (7 cases). Jaffe proposed that the positive potential prevented other sperm from interacting with the egg. This hypothesis was supported by the observation that eggs held positive by current injection could not be fertilized. All Jaffe’s experiments were carried out at one sperm density, approximately lo6 sperm/ml. To further test her hypothesis, the fraction of monospermic eggs could be measured at higher sperm densities. A major difference between Jaffe’s ex-

335

periments and ours is the measured resting potentials of eggs. Jaffe and Robinson (1978) have argued that the -lO-mV resting potential of sea urchin eggs seen by Steinhardt et al. (1971) and Ito and Yoshioka (1973) is due to damage of the egg plasma membrane. The majority of our resting potentials were between -8 and -16 mV. If eggswere left in seawater for several hours before impalement, a small fraction had resting potentials between -60 and -80 mV. Although we did not study this, it appeared that the fraction of eggswith large negative resting potentials increased with the length of time spent in seawater prior to impalement. Eggs with high resting potentials give a response similar to eggs with low resting potentials, except the amplitude of the first step is larger. In over 150 experiments, we have never recorded an initial event (step) in eggs greater than l- to 2-mV depolarization from rest. For S. purpuratus the threshold voltage for suppressing sperm entry at about lo6 sperm/ml is +lO to +5 mV (Jaffe, 1976). It is possible that the step depolarizations we see do alter the probability of the next successful collision, however, there is no obvious change in the pattern of long and short durations following the first step (for examples, see Figs. 1 and 2). A more difficult question (one we have not answered) is the comparison of the time between sperm exposure and the first step with the time between the first and all subsequent steps. At present, we can offer no evidence in Paracentrotus and Psammechinis for a fast electrically mediated block to polyspermy. If our impalements resulted in leaky membranes, such that the rapid depolarization Jaffe has correlated with a block to polyspermy could not occur, we should have expected our impaled eggsto be highly polyspermic. The results in Table 2 suggest that there is no significant difference in polyspermy between impaled and control eggs. If rapid depolarization were critical

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for preventing polyspermy, one should have seen a much larger difference. We are led, therefore, to look for alternative mechanisms of polyspermy prevention in this species of sea urchin. One possibility is that the frequency of successful collisions is really quite low. Obviously, the successful collision rate depends on the viable sperm concentration at the egg plasma membrane. In addition, the egg surface may change after the first successful collision, decreasing the probability of subsequent interactions. Rothschild and Swann (1952) suggested a fast partial block to polyspermy by comparing reaction rates of eggs with sperm at low and high densities. Their reaction rates were derived by assuming a specific model of sperm-egg interactions. This model has been criticized by Hultin (1956) and Hultin and Hagstrom (1956). However, the Rothschild and Swann interpretation of the kinetic data is accepted by most workers, and their derived rate of successful collision is comparable to our measured rate at low sperm densities (Dale et al. (1978) and this report). Rothschild and Swann (1951) found that the fraction of monospermic eggs in Psammechinus miliaris increased in time according to the relationship

VOLUME 72,1979

(1952), are shown in Fig. 4. Since (Y’ (the refertilization rate) was found to be much less than (Y (the monospermic rate), it was concluded that a rapidly acting partial block reduced the probability of successful reactions after the first had occurred. Since (Y’ in Eq. (2) is the rate of increase of polyspermic eggs, it is perforce an underestimate of the successful collision rate because it does not take into account the actual number of sperm per polyspermic egg. Rothschild and Swann (1951) suggest that the nonlinear dependence of cy on n may be due to sperm-sperm interactions which become more important at higher sperm densities. A similar factor should apply for the high sperm densities used to determine (Y’ and may contribute to the low values they obtained. The successful collision rates of sperm with oocytes agree reasonably well with the results of Rothschild and Swann (1951) below lo6 sperm/ml, but differ significantly at higher sperm densities. There is no fast block in oocytes since the successful collision rate increases continuously with the sperm density. As we have pointed out, the successful reaction rate in eggs is difficult to measure as one approaches lo7 sperm/ml because of the close spacing of steps. From Table 1 we may estimate an upper limit on the rate at M(t) = 1 - e-“’ (1) low sperm densities. The single step at 6.2 x lo5 sperm/ml occurred in the 13-set for sperm densities below 3 x 106/ml. M(t) shoulder phase, giving a maximum rate of is the fraction of monospermic eggs at time about 0.08 per sec. Increasing the sperm t, and (Y is a rate constant. Monospermy density lo-fold increases the rate to about and polyspermy were judged by normal and 3 per 13-set shoulder, or 0.23 per sec. These abnormal first cleavage. Their values for (Y as a function of sperm density are shown in values fit well with the oocyte data shown Fig. 4. At sperm densities between 7 X lo7 in Fig. 4. Higher sperm densities (Experiments 1 and 3 x 108/ml, for which eggs were genand 2 in Table 1) give four or five steps in erally polyspermic, a similar relationship the first few seconds of the shoulder region, was found: implying a rate of about one per second. These reaction rates suggest that in mature P(t) = 1 - e-“L. (2) eggs there is a monotonic increase in sucP(t) is the fraction of polyspermic eggs at cessful collision rates in the measurable time t, and (Y’ is a rate constant. The values range around lo6 sperm/ml, although stafor CX’, taken from Rothschild and Swann tistical variation is expected. These data

DEFELICE

AND DALE

Voltage Response to Fertilization

argue against a rapid permanent block in mature eggs but not necessarily against a fast partial block. In the Appendix, we shall consider three models of sperm-egg interactions. These are based on Fig. 5, in which trials by many sperm lead to successful reactions in sequence. We shall show that a rapidly acting partial block to polyspermy (model b) may have kinetics similar to a slow permanent block (model c). Case (a) is based on Scheme Al with all rate constants equal. This implies that there are no partial blocks, i.e., supernumerary sperm react with the same probability as the first fertilizing spermatozoon. If no permanent blocks exist, the number of monospermic eggs increases to a maximum and then decreases as supernumerary sperm react with the egg. The fractional change of monospermic eggsis given by Eq. (A7). Since Eq. (A7) predicts no monospermic eggs at long times, it disagrees with experiments done on eggs (Eq. (1)). The generalization of case (a) is given by Eq. (A4) and is the Poisson distribution for obtaining exactly s events if at is the average number of trials. Presley and Baker (1970) have used Eq. (A4) to predict the number of sperm per egg at different times following insemination. Their data disagreed with a Poisson distribution and they concluded that there must be a fast partial block to polyspermy. Although their findings provide additional evidence against

’ +--!k, IL/A0 --j FIG. 5. A schematic representation of an intracellular recording from an egg inseminated at t = 0. V is voltage and t is time. The arrows signify sperm collision; the first successful collision occurs with an average rate a~, or l/a0 set after the initial exposure to the sperm. The second step marks the second successful collision, l/e1 set after the first.

337

case (a), Presley and Baker give no direct evidence for a fast partial block. Case (b) introduces a partial block in the reaction Al by assuming that the second rate constant (al) is smaller than the first (cQ). The fractional increase in monospermic eggs is given by Eq. (All): N, -= N

a0 ao-al

(pf

_ ,-~I,~)~

(3)

The fractional increase in polyspermic eggs is given by Eq. (AlO): NP -= N

a0(1 - e-“‘l) - (~1(1 - e--uOL). (4) a0 - a1

Equation (3) is identical to Eq. (1) if a1 = 0 and a0 = (Y. Equation (4) is similar to Eq. (2) if a0 >> (Y~and LN = (Y’. In general, however, case (b) predicts no monospermic eggs at long times; eventually, all eggs become polyspermic. Case (a) or (b) may agree reasonably well with experiments in the period before the maximum number of monospermic eggs is reached; eventually these models must fail because they contain no permanent block. However, model (a) or (b) may correspond to the kinetics of oocyte fertilization since oocytes appear to have no mechanism for achieving permanent block to supernumerary sperm. Case (c) assumes that no partial blocks exist (all rate constants (Y are equal), but assumesthat an egg which has reacted with the first spermatozoon may go to a state of permanent block. This model is described by Scheme A12. A monospermic egg becomes permanently monospermic (indicated by an asterisk) if an average time l/ p expires before it reacts with a second spermatozoon. The fractional increase in permanently monospermic eggs is given by Eq. (A17): -N,* = (1 - emef) N - _ a a+Er

(5) (1 - e-t” + 8)‘).

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DEVELOPMENTALBIOLOGY

The final value of (N,*/N) is /?/(a + p). If the time to block (l/p) is short compared with the average time between successful collisions (l/a), Eq. (5) is identical to Eq. (1) and the fraction of permanently monospermic eggs approaches 100%. The fractional increase of polyspermic eggs is given by Eq. (Ala):

(6)

The final value of (N,/N) is a/(a + p); if /3 >> a, no polyspermy occurs. If /? is constant and (Y increases with n, the final ratio of monospermic to polyspermic eggs depends only on the sperm density. This is in agreement with experimental results. Obviously, a model that combines a partial block (b) and a permanent block (c) could also explain our results. The conclusion of our analysis is that a partial block, in itself, may be unnecessary. To test the hypothesis of a partial block, the average time between steps 1 and 2 (l/ (Y~ in Fig. 5) should be compared with the average time between exposure to sperm and the arrival of the first successful spermatozoon (l/a0 in Fig. 5). We have observed only that there is no apparent preference for the occurrence of steps following the first step. If there is no rapidly acting, partial block to polyspermy in Psammechinus and Paracentrotus, and the egg is vulnerable to supernumerary sperm during the 13-set shoulder period, how do sea urchins ensure a high number of monospermic eggs? A possible explanation is that under natural conditions the egg membrane is exposed to sperm concentrations which result in a successful collision rate comparable to the average time to block. The presence of the jelly coat has been shown to protect the egg against polyspermy (Hagstrom, 1956b) by reducing the number of sperm reaching the

VOLUME 72.1979

egg membrane by up to 90% (Hagstrom, 1959). Furthermore, we have observed that sperm have a decreased capacity to fertilize with time spent in seawater. These two mechanisms will reduce the number of viable sperm at the egg surface. Even when we decrease the effect of these factors, by using dejelhed eggs and fresh sperm, we observe surprisingly low rates of successful collision. At lo7 sperm/ ml the rate is about one every 3 sec. If egg jelly and sperm fertilizability were to reduce this rate by 10, even 60 set to permanent block implies that one-third of the eggs shall be monospermic (model c); lo7 sperm/ ml may not be unreasonable under natural conditions since it only implies a dilution between 100 and 1000 of dense white sperm released from the testes. It is, of course, possible that different species of sea urchin use different mechanisms to block polyspermy. We raise the point that a fast partial block may be unnecessary to achieve a high percentage of monospermic eggs in the species we have studied. APPENDIX

Models for Polyspermy in Sea Urchins Consider N eggs (or oocytes) exposed suddenly to a uniform and constant density of sperm. Assume that successful collisions result from a series of random trials; the egg treats repeated trials by the same spermatozoon the same as trials by other sperm. Let (Y be the average rate of successful collisions. We shall assume that (Yincreases with sperm density. A successful collision is marked by a step depolarization in the egg plasma membrane. The step lasts for a fixed time (13 set at room temperature). After this period, the membrane potential begins a continuous depolarization, probably signifying the beginning of the cortical reaction and the onset of permanent block to further sperm entry. If other sperm react with the egg during the initial step, they also produce step changes and eventually enter the egg.

DEFELICEANDDALE

Voltage

This is illustrated in Fig. 5 for the first and second steps; the average rate of trials is constant, but the probability of success is lower for the second sperm in this illustration. The measured rise time of a step is less than 200 msec. This is brief compared with the average time between successful encounters at normal sperm densities. Therefore, we exclude the possibility of simultaneous successful collisions and model fertilization as a series reaction. The kinetic scheme is described by No%? N+i

Nz ..- Ns,

339

to Fertilization

rate constants

equal (Y, are:

dNo = -UN,,, dt dN1 = aNo - aN1, dt

t-42)

dNz = aN1 - aN2, etc.

-

dt

The solutions

to these equations

are:

No(t) = Ne-“l, Nl(t)

= NateP,

Nz(t)

= NTebe2

(A3)

(Al)

where N,(t) is the number of eggs having s sperm at time t. Fertilization of sea urchins under natural conditions does not occur at a uniform and constant sperm density. The sperm density is being constantly diluted, and their capacity to fertilize decreases in time. Constant conditions may, however, be approximated in the laboratory. The kinetic data of Rothschild and Swann were obtained by dropping eggs into freshly prepared mixtures of sperm and seawater. Our data were obtained by dropping such mixtures directly on the experimental egg and obtaining our data within seconds of the initial reaction. Various theoretical cases are discussed below which correspond approximately to these experimental conditions. (a) No block to polyspermy. Consider the kinetic scheme (Al) with all rate constants equal: a0

Response

= al = (~2, etc.

In this case, the second, third, etc., sperm have the same chance of entering the egg as the first. Thus, there is no partial block to polyspermy. In this case, there is also no permanent block to polyspermy. Sperm continue to enter the egg at a rate proportional to the sperm density. This situation corresponds to the germinal vesicle stage of the sea urchin egg (see Fig. 4). The equations that describe (Al), if all

-d, etc

The general solution for the number of eggs that have reacted with s sperm at time t is: N,(t)

(4” = NTe

-&

.

(A4)

The number of fertilized eggs is the total number minus those that have not reacted: Nf(t)

= N - No(t) = N(l

- em,‘).

(A5)

The number of polyspermic eggs is the total number minus (No + N1): Np(t) = N[l The number ply NI: N,(t)

- (1 + at)eeat].

of monospermic = Nl(t)

(43)

eggs is sim-

= Natemat.

(A7)

The number of fertilized eggs and the number of polyspermic eggs increase continuously, however, the number of monospermic eggs goes through a maximum value when

t = l/a. The maximum eggs is

number

of monospermic

Nmmax = ! N, e or 37% of the total.

340

DEVELOPMENTAL BIOLOGY

The fractions of eggs which are fertilized, polyspermic or monospermic, are given by Eqs. (A5-A7). These correspond to the fractions which would be measured if the experiments were stopped at time t, e.g., by killing the sperm. (b) Partial block to polyspermy. Consider the kinetic scheme (Al) with a0 > al.

VOLUME 72,1979

pose all rate constants (Yare equal, but eggs that have accepted a single spermatozoon can go to a state of permanent block. (Eggs with more than one spermatozoon may also go to permanent block, but here we are not interested in their number.) Let the average rate to permanent block be /3. The kinetic scheme that described this situation is

No3 Nlq LP Nl*

(This case is illustrated in Fig. 5.) The equations that describe this situation are: dNo -

dt

=

-aoNo,

dN1 = aoN - alN1, etc.

b48)

dt

are: dNo = -aNo, dt

-

(A13)

LW

x, - aNl - PNl, -dN1 = LYIV,,

N,(t) =N

(A=)

where N1* (t) is the number of permanent, monospermic eggs. The equations that describe this model

The numbers of eggs that are fertilized, polyspermic or monospermic, are:

Nf(t) = N(l - e-@),

Nz.. .,

dt

(Yo(l - ema+)- all1 - e-ao’), a0

-

AL(t),= N&

(Alo)

and

dNl* dt

a1

-

(e-“1’ - e-“0’).

(All)

= ,bNl,

The solutions of these equations are:

As in case (a), Nf and NP increase continuously, however, the number of monospermic eggs has a maximum value. The maximum occurs when ln(ao/ad

Nl(t)

= N E

6415) (1 - emfit)e-“‘,

0P

(A16)

and

t= a0

No(t) = Ne-Ot,

-

a1

If (YO >> al, the number of monospermic eggs approaches 100%. The fractions of eggs implied by (A9All) correspond to those expected at time t if the experiments were stopped. At sufficiently long times, no monospermic eggs are expected for case (a) or (b) because neither model has a permanent block to supernumerary sperm. Although this disagrees with the kinetics of egg fertilization, it may describe oocyte fertilization. (c) Permanent block to polyspermy. Sup-

N1*(t) = N[(l - 2

- emat)

(A17)

(1 - e-(” + a)t)]e

The number of fertilized eggs is stilI described by Eq. (A9). The number of polyspermic eggs is:

N,(t) = N - [N,,(t) + Nl(t) + Nl*(t)].

(A18)

The number of eggs permanently monospermic and destined for normal development is given by Eq. (A17),

DEFELICE N,*(t)

Whereas

NI(t)

AND DALE

= NI*(t).

has a maximum

(Al%

value when

the number of permanently blocked spermic eggs increase continuously maximum value: NI

*max

Volt age Response

monoto a

=

This work was supported by C.N.R. Biology of Reproduction (to A. Monroy), and the Royal Society, London.

project on E.M.B.O.

REFERENCES BYRD, E. W., and COLLINS, F. D. (1975). Absence of fast block to polyspermy in eggs of sea urchin Strongylocentrotus purpuratus. Nature (London) 257, 675-677. DALE, B., DEFELICE, L. J., and TAGLIETTI, V. (1978). Membrane noise and conductance increase during single spermatozoon-egg interactions. Nature (London) 275,217-219. DEFELICE, L. J., and DALE, B. (1979). Membrane noise and successful collision rates studied during multiple sperm-egg interactions. Biophys. J. 25, 302a. EPEL, D. (1978). Mechanisms of activation of sperm and egg during fertilization of sea urchin gametes. Curr. Topics Develop. Biol. 12, 185-246. HAGSTRBM, B. E. (1956a). Studies on polyspermy in sea urchins. Ark. 2001. 10,307-315. HAGSTR~M, B. E. (1956b). The effect of removal of the jelly coat on fertilization in sea urchins. Exp. Cell Res. 10,740-743. HAGSTRBM, B. (1959). Further experiments on jellyfree sea urchin eggs. Exp. Cell Res. 17, 256-261. HAGSTRBM, B., and HAGSTR~M, B. (1954). The action of trypsin and chymotrypsin on the sea urchin egg.

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341

Exp. Cell. Res. 6, 532-534. HAGSTR~M, B. E., and ALLEN, R. D. (1956). The mechanism of nicotine induced polyspermy. Exp. Cell Res. 10, 14-23. HULTIN, E. (1956). Mechanism of fertilization by rate determinations. Exp. Cell Res. 10,286-293. HULTIN, E., and HAGSTR~M, B. E. (1956). The variability in the fertilization rate. Exp. Cell Res. 10, 294-308. ITO, S., and YOSHIOKA, K. (1973). Effect of various ionic composition upon the membrane potentials during activation of sea urchin egg. Exp. Cell Res. 78, 191-200. JAFFE, L. A. (1976). Fast block to polyspermy in sea urchin eggs is electrically mediated. Nature (London) 261, 68-71. JAFFE, L. A., and ROBINSON, K. R. (1978). Membrane potential of the unfertilized sea urchin egg. Develop. Biol. 62, 215-228. LBNNING, S. (1967a). Electron microscopic studies of the block to polyspermy. The influence of trypsin, soy bean trypsin inhibitor and chloralhydrate. Sarsia 30, 107-116. L~NNING, S. (1967b). Studies of the ultrastructure of sea urchin eggs and the changes induced at insemination. Sarsia 30, 31-48. PRESLEY, R., and BAKER, P. F. (1970). Kinetics of fertilization in the sea urchin: A comparison of methods. J. Exp. Biol. 52,455-468. LORD ROTHSCHILD (1954). Polyspermy. Quart. Rev. Biol. 29, 332-343. LORD ROTHSCHILD, and SWANN, M. M. (1949). The fertilization reaction in the sea urchin egg. A propagated response to sperm attachment. J. Exp. Biol. 26, 164-181. LORD ROTHSCHILD, and SWANN, M. M. (1951). The fertilization reaction in the sea urchin. The probability of a successful sperm-egg collision. J. Exp. Biol. 28,403-416. LORD ROTHSCHILD, and SWANN, M. M. (1952). The fertilization reaction in sea urchin. The block to polyspermy. J. Exp. Biol. 29,469-483. STEINHARDT, R. A., LUNDIN, L., and MAZIA, D. (1971). Bioelectric responses of the Echinoderm egg to fertilization. Proc. Nat. Acad. Sci. USA 68,2426-2430.