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B
A
Vitelline
envelope

Egg cell
membrane
Cortical granules Enzymes from
cortical granules




Supernumerary
sperm
C
Microvilli
Sperm
tail
Newly fertilized egg

Contents of
cortical granules
Sperm released
from
surface
D

Fertilization envelope
Hyalin


Fig. 9.7 Schematic illustration of the steps involved in the slow block to polyspermy.
The leftmost panel gives a three-dimensional representation of a fertilized egg (the
microvilli are shown at a larger than true scale) with the tail of the fertilizing
spermatozoan (or sperm) protruding from it. Panels A“D show the cortical reaction at
successive times following fertilization (viewing the interior of the egg through the cut
indicated). Prior to the stage shown in panel A the fertilizing sperm has penetrated the
vitelline envelope by means of the acrosome reaction (see Fig. 9.5), and its plasma
membrane has fused with the egg plasma membrane (see the main text for a description).
This membrane fusion initiates the cortical reaction. (A) Three supernumerary
(non-fertilizing) sperms approach the vitelline envelope. Beneath the egg-plasma
membrane cortical granules move along radial actin micro¬laments (magenta) toward the
inner surface. (B, C) These granules fuse with the plasma membrane and release their
contents, enzymes that cleave the protein bridges connecting the vitelline envelope to
the egg-plasma membrane, as well as the protein hyalin, osmotically active proteoglycans
that cause water to enter the perivitelline space and swell the vitelline envelope, and
additional enzymes that cause the newly deposited ECM to harden. (D) The resulting
matrix, the “fertilization envelope,” prevents further penetration of the supernumerary
sperms, which are consequently released from the egg surface. (After Gilbert, 2003.)
238 BIOLOGICAL PHYSICS OF THE DEVELOPING EMBRYO


space (see Fig. 9.2) between the egg™s plasma membrane and the egg™s
ECM (e.g., the zona pellucida) provides a barrier, termed the fertil-
ization envelope, to additional sperm entry. This is the slow block to
polyspermy, and it happens in virtually all species studied. Then, de-
pending on the species, successive waves of calcium ion concentra-
tion go on to trigger other events of early development. In mammals
these include the completion of meiosis, the initiation of mitosis, the
initiation of protein synthesis from stored maternal mRNAs (Runft
et al., 2002) and the initiation of surface waves of cortical contractil-
ity (Deguchi et al., 2000) (Fig. 9.8).




Fig. 9.8 A traveling wave of Ca2+ concentration (colors) and cytoplasmic movement
(black-and-white) during the rising phase of the initial Ca2+ wavefront in the mouse egg,
following fertilization. The position of the sperm-fusion site and that of the animal pole
are indicated by arrows labeled “sp” and “AP” respectively in the bright-¬eld image
(second row, at the left). The egg was loaded with the Ca2+ -sensitive dye calcium
green-1 dextran and subjected to ¬‚uorescence microscopy. The (pseudo-)colors
represent the intensity of the emitted ¬‚uorescence, relative to a basal value (see the
color bar at the bottom right), obtained from images just before the rise in Ca2+
concentration. The number shown at the bottom left of each image is the time (in
seconds) of acquisition. The zero of time is de¬ned by the time when the image for the
basal value of ¬‚uorescence was taken, before the initial rise in intensity. The arrows in
the black-and-white images represent the direction and magnitude of the local
cytoplasmic velocity, as detected from the analysis of the time series of bright-¬eld
images taken at 0.5 s intervals (for reference see the arrow at the bottom right). After
the reference image at 106 s only the contour of the egg and selected lattice points,
approximately 11 micrometers apart, are shown. (Reprinted from Deguchi et al., 2000,
with permission from Elsevier.)
9 FERTILIZATION: GENERATING ONE LIVING SYSTEM FROM TWO 239


Unlike the ion transients that occur during the fast block to
polyspermy, the source of which is in the external medium, the source
of ions for the later calcium transients is in intracellular ˜˜stores”
(Bugrim et al., 2003), membranous compartments that are under the
control of intracellular signals, most notably inositol trisphosphate
(IP3 ) (Berridge et al., 2000). Once the release of these stores has been
initiated in the fertilized egg, a periodic series of self-sustaining waves
of elevated Ca2+ concentration travel through the egg™s cortical cyto-
plasm (Kubota et al., 1987; Miyazaki et al., 1993; Eidne et al., 1994;
Jones, 1998; Deguchi et al., 2000; Dumollard et al., 2002). Several of
the major postfertilization events mentioned above are initiated by
different numbers of Ca2+ waves, while their completion requires a
greater number of Ca2+ waves than their initiation (Ducibella et al.,
2002). This suggests that there is informational content in the spon-
taneous Ca2+ waves that follow fertilization. Moreover, it seems that
a single dynamically organized signaling system can regulate the dif-
ferent cellular events associated with early development that must
occur in a distinct temporal sequence.

Modeling Ca2+ oscillations in the egg
Concomitant with the transient depolarization of the egg™s plasma
membrane brought about by the fusion of the egg and sperm is an
approximately ten-fold increase in the intracellular calcium ion con-
centration of the egg. This increase occurs (depending on the species)
in the form of one or more traveling waves of elevated Ca2+ , which
start at the point of sperm entry. The initial effect of the elevated
calcium ion concentration is the triggering of the cortical granule
reaction, in the course of which these organelles beneath the plasma
membrane fuse with it and discharge their protein contents. This
process establishes the slow block to polyspermy (Jaffe et al., 2001), as
discussed above. The initial and subsequent waves, in species where
they occur, cause major intracellular restructuring and eventually
bring the postfertilization machinery into motion.
Transmitting information in the form of calcium oscillations is
a ubiquitous means of both intercellular and intracellular signaling.
Experimental evidence indicates that both the temporal and the spa-
tial behavior of these oscillations has information content. Strikingly,
the magnitude of their frequency (typically in the range 10’3 --1 Hz)
and amplitude controls the speci¬city of gene expression (Dolmetsch
et al., 1998), which may, in turn, activate the initial developmental
events.
The fertilization wave, as observed in sea urchins or Xenopus, is
a continuous wave of well-de¬ned amplitude, which sweeps through
the egg in a short time (around 30 seconds in the sea urchin (Hafner
et al., 1988) and 2.5 minutes in Xenopus (Fontanilla and Nuccitelli,
1998)). The generation and propagation of these waves is due, as noted
above, to the release of calcium ions from the endoplasmic reticu-
lum, which is triggered when the cytosolic concentration of the ions
reaches a threshold value, a phenomenon known as Ca2+ -induced
240 BIOLOGICAL PHYSICS OF THE DEVELOPING EMBRYO


Ca2+ release. At the threshold, specialized channels (i.e., IP3 recep-
tors) are activated. These channels are inactivated as the local Ca2+
concentration rises further and subsequently remain closed during
a refractory period. Finally, cytosolic Ca2+ is resequestered into the
endoplasmic reticulum via specialized pumps.
It is not entirely clear what initiates the fertilization calcium wave
(Dumollard et al., 2002). According to one hypothesis, the transient in-
crease in calcium concentration at the point of sperm entry is due
to the release of Ca2+ by the sperm itself (Stricker, 1999). Another
proposal is that an as yet unidenti¬ed ˜˜sperm-factor” activates local
calcium release upon fusion of the sperm™s and egg™s plasma mem-
branes (Oda et al., 1999; Sardet et al., 1998; Stricker, 1999; Jaffe et al.,
2001). It is also possible that the interaction of the sperm and the egg
activates a special class of receptors on the egg surface and that this
results in the production of IP3 , which opens IP3 -dependent calcium
channels in the egg™s endoplasmic reticulum near the fertilization
site (Miyazaki et al., 1993; Stricker, 1999; McDougall et al., 2000). Ex-
perimental results seem to favor this last hypothesis (Bugrim et al.,
2003).
The activation of Ca2+ -releasing channels by a threshold concen-
tration of cytosolic Ca2+ is another manifestation of the nature of
the cell as an excitable medium (Lechleiter et al., 1991, 1998). Nu-
merous models have been constructed to describe the formation
and propagation of calcium oscillations (for a review see Schuster
et al., 2002). As we have seen in Chapter 5, to describe excitability
mathematically, nonlinear differential equations are needed. A rela-
tively simple model of this sort, the ˜˜¬re--diffuse--¬re” (FDF) model of
Dawson et al. (1999), gives an account of the formation and propaga-
tion of continuous postfertilization calcium waves.
In the FDF model the release of calcium from the intracellular
stores is assumed to take place through an array of release sites rep-
resented by point sources corresponding to actual storage vesicles
with regulated channels. (A similar model was discussed by Bugrim
et al., 1997). These sites are spaced at a distance d from one another
and are embedded in a continuum (the cytosol) in which calcium
ions are assumed to diffuse. The release of calcium takes place while
a channel is open, which de¬nes the chemical time scale „ . Another
time scale (the intersite diffusion time) is de¬ned by d 2 /D (cf. Eq. 1.1),
where D is the Ca2+ diffusion coef¬cient. Whenever the cytosolic
Ca2+ concentration in the vicinity of a release site reaches a thresh-
old value [Ca2+ ]T above the basal concentration [Ca2+ ]B , the site starts
releasing calcium ions at a rate σ/„ . Here σ is the total number of
ions released in time „ by a single site. (Some of the released calcium
ions are buffered by binding to proteins and thus do not participate
in wave generation and propagation. This is incorporated into the
model by using a number smaller than σ and a buffered diffusion
coef¬cient, details we will ignore here.)
Ca2+ release and diffusion is described by a single nonlinear
equation, which is a reaction--diffusion equation similar to those
9 FERTILIZATION: GENERATING ONE LIVING SYSTEM FROM TWO 241


encountered in Chapters 7 and 8 (details can be found in Dawson
et al., 1999, and in Pearson and Ponce-Dawson, 1998). Mathematical
analysis shows that the dynamics depends on only two dimensionless
parameters (instead of the six parameters d, „ , D , σ , [Ca2+ ]T , [Ca2+ ]B
introduced above), de¬ned by the following expressions:
σ/d 3
= , (9.8)
[Ca2+ ]T ’ [Ca2+ ]B


D„
β= . (9.9)
d2
The meaning of these parameters is easy to understand. Since σ/d 3
is the release concentration (the amount of Ca2+ released per site
divided by the volume per site), is the ratio of the release concen-
tration to the difference between the threshold and basal concentra-
tions. Intuitively it is clear that no traveling wave can be sustained
if < 1. The parameter β is the ratio of the time for which a site
is open, „ , to the intersite diffusion time d 2 /D . This parameter con-
trols the shape of the propagating wave. If the chemical reaction
involved in release is the rate-limiting process (the ˜˜reaction-limited”
case, „ d 2 /D ) then β 1 and the wave is continuous. If β 1, the
˜˜diffusion-limited” case, the wave is saltatory (i.e., it has an abruptly
changing shape). In the former case the wave travels without observ-
able change in its shape, whereas in the second case its shape changes
in time.
Using experimental results for „ , d, D , σ , [Ca2+ ]T , and [Ca2+ ]B , the
FDF model predicts that the fertilization wave in Xenopus is a con-
tinuous wave, in accord with the experimental ¬ndings (Fontanilla
and Nuccitelli, 1998) and has the shape shown in Fig. 9.9. (Saltatory
waves have been observed in Xenopus oocytes prior to fertilization;
Callamaras et al., 1998).
In summary, the FDF model emulates the active process of calcium
wave propagation by a combination of the passive diffusion of Ca2+
and its active release from point-like sources. This is a reasonable rep-
resentation of the biological reality. As discussed in Chapter 1, in the
crowded intracellular environment simple diffusion can be a viable
transport mechanism only on a limited spatial scale, even for small
molecules such as Ca2+ . In the FDF model the cytosol is assumed to
be homogeneous apart from point-like release sites and thus inter-
site diffusion is assumed to be unhindered. The close spacing of the
sites, however, ensures that free diffusion takes place only between
the release sites and therefore on a small spatial scale. On the scale
of the entire egg the reinforcement of the wave by Ca2+ -induced Ca2+
release is an active process. The important message from the work of
Dawson et al. (1999) is that a relatively simple model based on biologi-
cally plausible assumptions can explain the excitable character of the
zygote (with respect to Ca2+ wave generation and propagation) and
provide testable predictions of the shape of postfertilization calcium
waves.
242 BIOLOGICAL PHYSICS OF THE DEVELOPING EMBRYO


0.9



0.8



0.7




[Ca ] (µM)
0.6



+2
0.5



0.4

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