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according to the above analysis, the net force acting on it perpen-
dicular to the direction of motion is zero.) In some marine species,
in which the sperm navigates using a species-speci¬c chemotactic
gradient produced by the egg (Yoshida et al., 1993), and perhaps in
mammals as well (Spehr et al., 2003), the gradient sets the direction
of the sperm™s velocity vector, for which the sperm itself, using the
mechanism described, supplies the vector™s magnitude.
9 FERTILIZATION: GENERATING ONE LIVING SYSTEM FROM TWO 233



Interaction of the egg and sperm
Once the sperm arrives at the egg it has to penetrate its ECM (vitelline
membrane, jelly coat, zona pellucida) and fuse with its plasma mem-
brane. The initial interaction, in species as varied as fruit ¬‚ies, clams,
sea urchins, and humans, is the acrosome reaction. This sudden exo-
cytotic event, in which the acrosomal vesicle fuses with the sperm
plasma membrane, spilling out its enzyme contents (Fig. 9.5), is trig-
gered by the binding of proteins and/or glycoproteins in the api-
cal membrane of the sperm to glycoproteins of the egg ECM (Was-
sarman, 1999). The sperm then moves through the ECM until its
new apical membrane, previously the ˜˜¬‚oor” of the acrosomal vesi-
cle, meets up with the egg™s plasma membrane and fuses with it.
This event, called ˜˜syngamy,” permits the sperm nucleus, also called
the male ˜˜pronucleus,” to enter the egg, where it meets up with
the female pronucleus. (In mammals, the second meiotic division
must take place before the female pronucleus can form.) Once these

Sperm cell Fusion of
membrane sperm cell membrane
and acrosomal
membrane
Acrosomal
membrane




Nucleus


Centriole



Fig. 9.5 Schematic illustration of the acrosome reaction in a mammalian sperm. The
bounding membrane of the acrosome (a large intracellular vesicle) and the apical region
of the sperm-plasma membranes fuse, forming discontinuous vesicles and thereby
releasing the ¬‚uid contents of the acrosome (orange). This ¬‚uid contains enzymes that
locally break down the zona pellucida (the vitelline envelope) of the egg, permitting the
sperm-plasma membrane, which remains intact throughout the acrosome reaction, to
approach and eventually fuse with the egg-plasma membrane (see also Fig. 9.7). (After
Yanagimachi and Noda, 1970.)
234 BIOLOGICAL PHYSICS OF THE DEVELOPING EMBRYO


haploid pronuclei join together, the fertilized egg contains the
genome of a new diploid individual. It is now termed a ˜˜zygote,”
and is ready to begin the series of cleavages described in Chapter 2.
Typically, thousands of sperms reach the egg more or less simul-
taneously. If more than one male pronucleus is deposited into the
egg™s cytoplasm (a situation known as ˜˜polyspermy”), the amount of
genetic material and number of chromosomes would be uncharacter-
istic of the species and the gene expression levels (which often differ
for maternally and paternally contributed versions of a gene) would
be unbalanced. Polyspermic zygotes are not viable, and two major
protective mechanisms have evolved to prevent this from occurring:
a ˜˜fast block” to polyspermy, triggered by sperm--egg surface contact
and involving a transient electrical change in the egg™s plasma mem-
brane (Glahn and Nuccitelli, 2003); and a ˜˜slow block” to polyspermy,
triggered by a self-organized traveling chemical wave, leading to exo-
cytosis of the egg™s cortical granules and the secretion of a long-lived
ECM barrier (Sun, 2003).

Membrane potential and the fast block to polyspermy
A few seconds after the ¬rst sperm binds, the egg™s resting electric
membrane potential, which is typically negative (about ’70 mV for
the sea urchin), shifts to a positive value of about +20 mV. This is
accomplished by the opening of sodium ion channels (for the compo-
sition of the plasma membrane see Chapter 4), which allows the in-
¬‚ux of Na+ . (Note that by convention the electric potential difference
across the plasma membrane is measured relative to the extracellular
milieu). Sperms cannot fuse with a plasma membrane having a posi-
tive resting potential. The sudden change in the membrane potential
provides a fast block to polyspermy, but it is transient: after a few
minutes its original value is reestablished.
The importance of the electrical potential difference in the fast
block to polyspermy was con¬rmed by experiments in which an elec-
trical current was arti¬cially supplied to sea urchin eggs in such a
way that their membrane potential was kept negative; under these
circumstances polyspermy resulted (Jaffe, 1976). Although the molec-
ular details of how the sperm triggers electrical changes at the egg
surface are not well understood, the physics of all such membrane
phenomena are governed by a fundamental mechanism described by
the Nernst--Planck equation, which determines the value of the mem-
brane™s resting potential.
Ultimately, it is the ions in the close vicinity of the membrane,
held there by their electrical attraction to the oppositely charged
counter-ions, that give rise to its potential (Fig. 9.6). Ions can move
across the membrane, through speci¬c ion channels, for two distinct
reasons: there must be an imbalance either in the concentration of
particular ions (i.e., a concentration gradient) or in the net charge (i.e.,
an electric ¬eld gradient) between the two sides of the membrane. It
is easy to see that these two gradients lead to opposite effects. Dif-
fusion along a concentration gradient will move molecules from the
9 FERTILIZATION: GENERATING ONE LIVING SYSTEM FROM TWO 235



Exact balance of charges:
Membrane potential = zero
+-+- +-+- -
+
-
+
-+-+ -+-+ -
+ +
-
+-+- +-+- -
+
-
+
-+-+ -+-+ -
+ +
-
+-+- +-+- -
+
-
+
-+-+ -+-+ -
+ +
-
+-+- +-+- -
+
-
+
-+-+ -+-+ -
+ +
-


Separated counter-ions:
Membrane potential = zero
+-++ --+- -
+
-
+
-+-+
-+-+ -
+ +
-
--+-
+-++ -
+
-
+
-+-+
-+-+ -
+ +
-
+-++ --+- -
+
-
+
-+-+
-+-+ -
+ +
-
+-++ --+- -
+
-
+
-+-+ -
+ -+-+ +
-


Fig. 9.6 Origin of the membrane potential. A nonzero potential across the membrane
arises when the balance of charges on its intracellular and extracellular sides (upper
panel) is disrupted by the migration of a few positive (or negative) ions through the
membrane, leaving negative (or positive) counter-ions behind (lower panel).



higher concentration side to the lower one. If the molecules carry
charge, as in the case of ions, this motion will lead to a charge im-
balance and thus to an increase in the electric ¬eld gradient, which,
in turn, will resist the motion due to the concentration gradient. The
¬‚ow of ions is thus driven by the combination of the two gradients,
namely, the electrochemical gradient introduced in Chapter 1. When
the electrochemical gradient is zero there is no net ¬‚ow of ions. The
electric potential difference at which this equilibrium is established
is the resting, or equilibrium, membrane potential.
A nonzero electrochemical gradient implies a particle current (see
Chapter 1)
c(x)
j(x) = ’D + vd c(x). (9.5)
x
(Note that for simplicity we have assumed a steady, time-independent,
concentration.) The ¬rst term on the right-hand side of Eq. 9.5 is the
diffusion current, the second is the current due to external forces
236 BIOLOGICAL PHYSICS OF THE DEVELOPING EMBRYO


(see Chapter 1). In the case of the movement of ions with charge q
due to electric forces, the drift velocity (also introduced in Chapter 1)
is vd = F / f = q E / f = µE , where E is the electric ¬eld established by
the ion distribution and µ is the ion mobility. Equation 9.5 implies
the presence of a single ionic species, with diffusion coef¬cient D
and charge q. If there are several types of ions, each will be repre-
sented by a separate term in Eq. 9.5. For simplicity we assume that
there are two kinds of ions with opposite charge q+ = ’q’ = q and
corresponding diffusion coef¬cients D + and D ’ . We also assume that
the concentration gradients of these two ions are equal. Thus, using
the Einstein--Smoluchowski relation, D = kB T / f and the relationship
between the electric ¬eld and potential E = ’ V / x, Eq. 9.5 takes
the form
D+ ’ D’
V ln c(x)
j(x) = ’qc(x)(µ+ ’ µ’ ) + . (9.6)
µ+ ’ µ’
x x
Here ˜˜ln” stands for the natural logarithmic function and we have
used the relation
c ln c
= .
cx x
Finally, at equilibrium, for which j = 0,
D+ ’ D’ ci
V = Vi ’ Vo = ’ ln , (9.7)
µ+ ’ µ’ co
where the subscripts i and o refer to the inside and the outside of
the cell respectively. Equation 9.7 is called the Nernst--Planck equation
and the ratio of the concentrations, c i /c o , is the Donnan ratio. In the
hypothetical case when the membrane potential is due to a single
positively charged ionic species, Eq. 9.7 can be written as
’kB T ci
Vi ’ V o = ln ,
q co
Since the logarithmic function varies slowly with its argument and
for realistic concentrations gives a number of the order unity, the
resting potential (for ions at 37 —¦ C having unit positive charge) is
determined by the factor kB T/q = 26.7 mV. The resting potential for
most membranes other than the fertilized egg is indeed around this
value and varies between ’20 and ’200 mV.


Propagation of calcium waves: spatiotemporal
encoding of postfertilization events
The electrical fast block to polyspermy, which has been quantitatively
studied in sea urchins (Jaffe, 1976) and frogs (Cross and Elinson, 1980),
probably does not occur in mammalian eggs (Jaffe and Cross, 1986).
Even in species in which it occurs, it is transient: the membrane
potential of the fertilized sea urchin egg remains positive for only
about a minute (Jaffe and Cross, 1986; Glahn and Nuccitelli, 2003).
9 FERTILIZATION: GENERATING ONE LIVING SYSTEM FROM TWO 237


However, within a minute after sperm--egg fusion another sequence
of ion-dependent events takes place (this time involving calcium ions,
Gilkey et al., 1978), leading ¬rst to the concerted release of the con-
tents of the cortical granules -- the ˜˜cortical reaction” (Fig. 9.7). The
exocytosed material that thereby comes to lie in the perivitelline




Actin
Protein microfilaments
Sperm bridges

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