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size, both in its cytoplasmic compartment and in its nucleus (termed
the ˜˜germinal vesicle”). While the germinal vesicle contains only a
haploid complement of chromosomes, its genome is typically tran-
scriptionally active, producing many different types of RNA molecules
(Bachvarova, 1985; Picton et al., 1998). In some cases, such as Xeno-
pus and other amphibians, the requirement for ribosomes during the


to separate, remaining attached only by their centromeres (see Chapter 2). Since the
two-stranded nature of the individual chromosomes of the bivalents is now apparent, the
resulting “double“double” structures are referred to as “tetrads.” At this stage
“crossing-over” also takes place. Crossing-over refers to the process by which
corresponding portions of homologous chromosomes are exchanged with each other,
yielding chromosomes distinct from those contributed by either of the individual™s
parents. At the following stage, diplotene, the two chromosomes in each tetrad begin to
repel one another. Prophase I ends with diakinesis, in which the nuclear envelope breaks
down and the mitotic spindle ¬bers form. Meiosis I (middle panel) is a sequence of steps
analogous to mitosis in somatic (non-meiotic) cells, with an important difference. Rather
than the sister chromatids being separated during this process, the homologs are
separated. This leads to haploid daughter cells, i.e. cells that contain only one version of
each chromosome of a homologous pair. In spermatogenesis, the two daughter cells
resulting from meiosis I are of equal size and are called secondary spermatocytes. In
oogenesis, the division is uneven, the larger cell is called the secondary oocyte and the
smaller one the ¬rst polar body. Meiosis II (bottom panel) begins as these cells enter
prophase (not shown) directly, without undergoing S-phase, the DNA having already
been replicated in the S-phase immediately preceding meiosis I. This is followed by
anaphase II and telophase II (not shown) and then metaphase II. Meiosis II is similar to
somatic cell mitosis: the sister chromatids split apart and are partitioned into daughter
cells. In spermatogenesis, these cells are called spermatids; the original primary
spermatocyte yields four of them. Each spermatid undergoes a series of morphological
changes (spermiogenesis) to produce a mature gamete, the spermatozoon, or sperm. In
oogenesis, meiosis II, like meiosis I, is asymmetric, yielding a single ovum or egg, the
single gamete arising from the primary oocyte, and two other polar bodies.
228 BIOLOGICAL PHYSICS OF THE DEVELOPING EMBRYO


early cleavage stages leads to a several-thousand-fold ampli¬cation of
the number of copies of the genes specifying ribosomal RNA in the
oocyte nucleus during oogenesis (Thiebaud, 1979).
The end result of oogenesis is a large cell (the human and sea
urchin eggs are on the order of 100 m in diameter, that of Xenopus
is up to 2 mm, and the average length of the two main axes of the
ellipsoidal chicken egg is about 5 cm). Yolk consists of energy-rich nu-
trient molecules, and the amount required for development depends
on the species™ biology. Mammalian embryos get almost all their nour-
ishment from the maternal blood supply, so the eggs that give rise to
them contain very little yolk. Birds™ eggs, which develop outside the
mother™s body, contain huge amounts of yolk. Another typical feature
of eggs is an array of secretory vesicles in the cortical region of their
cytoplasm, which fuse with the plasma membrane once fertilization
occurs. The contents of these ˜˜cortical granules” -- primarily glyco-
proteins -- provide a barrier to the entry of additional sperms (see
below). Finally, the terminally differentiated egg is also surrounded
by an extracellular matrix (ECM) layer, consisting of various glycopro-
teins and other molecules (Wassarman et al., 1999), which is termed,
depending on the species, the ˜˜jelly coat” (sea urchins, amphibians),
the ˜˜vitelline membrane” or ˜˜vitelline envelope” (¬sh, birds), and the
˜˜zona pellucida” (mammals) (Fig. 9.2).
Spermatogenesis is completed by a ¬nal series of steps, termed
spermiogenesis, which gives rise to the morphologically de¬nitive
motile sperm cell, also called the ˜˜spermatozoon.” During spermio-
genesis the sperm loses most of its cytoplasm, develops an extended
¬‚agellum, retains its mitochondria, which generate ATP to drive the
¬‚agellar motion (although the mitochondrial DNA does not, at least
in mammals, get transmitted to the next generation of organism),
and develops a single apical secretory vesicle, the acrosome, which
contains enzymes, released during fertilization in a dramatic exocy-
totic event (the ˜˜acrosome reaction”), that facilitate penetration of
the sperm through the egg™s ECM (Fig. 9.3).

Physics of sperm locomotion
For the sperm to arrive at the egg it has to overcome the vis-
cous drag it experiences either in sea water (marine vertebrates and


Fig. 9.2 Cross-section of the egg
First polar body
of a mammal; see the main text for
details. (After Gilbert, 2003.)
Perivitelline space


Zona pellucida


Cortical granule


Meiotic spindle


Plasma membrane
9 FERTILIZATION: GENERATING ONE LIVING SYSTEM FROM TWO 229




Fig. 9.3 Principal components of a mammalian spermatozoon. The top right panel
shows a three-dimensional rendition of the entire spermatozoon; the top center panel
indicates the anatomical designations of its three main portions. The top left panel shows
a schematic of a cross-section of the sperm head with characteristic subcellular
components labeled. Exocytosis of the acrosome (see Fig. 9.5) enables the sperm to
penetrate the vitelline membrane (see Fig. 9.2) and brings the lower region of the sperm
cell membrane into contact with the egg cell membrane, with which it fuses. The sperm
nucleus is incorporated into the zygote; the single, coiled sperm mitochondrion is not.
The axonemal complex is the contractile assembly of the sperm tail ¬‚agellum. Sections
through the middle piece (B) and the tail (A) are shown in detail in the two lower panels,
where the relative locations of the mitochondrion and the microtubular components of
the axonemal complex are represented. (After Ross et al., 2003.)




invertebrates) or in the female reproductive tract (mammals, insects).
The extent to which the sperm™s own propulsive activity contributes
to its translocation toward the egg differs with different species. In a
watery environment external to the female™s body (e.g., in sea urchins
or ¬sh), the inherent motility of the sperm is all important. In the
reproductive tract of a female mammal other factors dominate at
230 BIOLOGICAL PHYSICS OF THE DEVELOPING EMBRYO


early stages of transport, such as the wave-like muscular movements
of the oviduct wall and perhaps the convective ¬‚ow of the sperm and
their surrounding matrix, hypothesized earlier in relation to dispers-
ing mesenchymes such as neural crest mesenchymes and PGCs. The
motility of the individual sperm is clearly decisive at certain points in
the transport of even mammalian sperm. Human males with Karta-
gener immotile-cilia syndrome (discussed in Chapter 8 in relation
to situs inversus), who lack the mechanical-force-transducing protein
dynein in their cilia and ¬‚agella (see below), have immotile sperms
and are infertile (Afzelius, 1985). The infertility is strictly a function
of the defective ¬‚agella: when sperm from these men are injected
directly into the egg, apparently normal births may occur (Cayan
et al., 2001).
When the sperm locomotes under its own power it does so by
means of its ¬‚agellar motor. In a bacterium, whose ¬‚agellum is a
more-or-less rigid helix, the motor is rotary: the bacterium moves
by the rotation of its ¬‚agellum about its own axis (Berg, 1993). In
eukaryotic cells, such as a sperm, the ¬‚agellum is a ¬‚exible rod
(Fig. 9.3). It is propelled into motion by a translational motor, the
details of which are poorly understood (Vernon and Woolley, 1995;
Woolley and Vernon, 2002). This motor produces ¬‚agellar beating
in the form of a more or less sinusoidal wave, which passes along
the length of the ¬‚agellum from the cell body towards the tail
(Fig. 9.4A).
As the sperm moves forward, driven by its ¬‚agellar motor, which
is fueled by the sperm™s metabolic energy, each segment of its ¬‚a-
gellar rod displaces perpendicular to the direction of locomotion
(Fig. 9.4B); this is a characteristic of a transverse wave. As we shall see it
is the speed of this transverse displacement that eventually generates
the forward-oriented velocity and the overall propulsion through the
¬‚uid. How can transverse oscillations in a viscous medium produce
forward motion? To understand this phenomenon, which is analo-
gous to the motion of a rocket, requires only Newton™s third law:
every action creates an equal and opposite reaction. As the sperm
moves it perturbs the liquid around itself. This results in a wave that
travels with its own wave velocity opposite to the direction of the
sperm™s movement, as indicated in Fig. 9.4A. Motion in a viscous liq-
uid, even with constant velocity, requires force. The force that propels
the sperm to move in one direction (to the right in Fig. 9.4A) is the
reaction force to the force pushing the wave in the opposite direction
(to the left in Fig. 9.4A).
For a simple physical model of sperm locomotion, consider
Fig. 9.4B, which shows two small segments of length l of the ¬‚ag-
ellar rod (of diameter d) separated by half a wavelength. In keeping
with the transverse wave motion these segments move in opposite
directions in the plane of the page, the instantaneous angles of the
up-moving and down-moving segments to the direction of locomotion
being θ and ’θ respectively. We now decompose the transverse speed v
9 FERTILIZATION: GENERATING ONE LIVING SYSTEM FROM TWO 231



Wave velocity

A
Direction of locomotion


B
v

-v -



D
C v 1

v F3
v 4

2
F
l




Fig. 9.4 (A) A schematic illustration of sperm locomotion. Flagellar beating in the
viscous medium produces sinusoidal wave-like propagation to the left, which in turn
propels the sperm to the right, by Newton™s third law. (B) Individual ¬‚agellar segments of
length l with velocities v and ’v , separated by half a wavelength; the segments form
angles θ and ’θ respectively with the direction of the sperm motion. (C)
Decomposition of the left-hand segment™s motion into parallel and perpendicular
component velocities v || and v ⊥ . (D) Decomposition of the viscous forces acting on the
segments into parallel and perpendicular components, F || and F ⊥ .



into components parallel (v || ) and perpendicular (v ⊥ ) to the axis of the
segment, as shown in Fig. 9.4C. We thus have

v || = v sin θ, (9.1)
v ⊥ = v cos θ. (9.2)

As we have seen in Chapter 1, an object moving under friction ex-
periences a drag force F that is oriented opposite to the direction
of motion and is proportional to the velocity of the object: F = f v.
In particular, if the motion takes place in a liquid, the friction con-
stant f is proportional to the viscosity of the liquid and strongly de-
pends on the shape of the moving object (see Eqs. 1.2 and 1.3). Thus,
associated with each velocity component of the segments shown in
232 BIOLOGICAL PHYSICS OF THE DEVELOPING EMBRYO


Fig. 9.4B is a viscous drag: F || = f|| v|| and F ⊥ = f⊥ v⊥ (Fig. 9.4D). Here
the friction constants f|| and f⊥ are given in Eq. 1.3. The expressions
in Eq. 1.3 are valid for a cylindrical body whose length (l) is much
larger than its diameter d. Since the diameter of the ¬‚agellar rod is
small, the condition l/d 1 is ful¬lled for the ¬nite small segments
in Fig. 9.4B. Moreover, as indicated by Eq. 1.3, for any ¬nite large value
of l/d we have f⊥ > f|| , which for a tilt angle θ ≈ 45—¦ (when v⊥ ≈ v|| )
implies that the force needed to move the ¬‚agellar segment perpen-
dicular to its axis is larger than that needed to move it parallel to its
axis. (In reality the tilt angle is considerably smaller than 45—¦ , which
makes F ⊥ /F || even larger.) It is exactly this disparity between F ⊥ and
F || that makes sperm propulsion possible.
We now decompose F ⊥ and F || for the up-moving segment in
Fig. 9.4B into components along the direction of sperm locomotion
(vectors 1 and 4 in Fig. 9.4D) and perpendicular to it (vectors 2 and 3
in Fig. 9.4D). Thus the net force acting on the ¬‚agellar segment as it
moves to the right is

F ’ = F ⊥ sin θ ’ F || cos θ = ( f⊥ ’ f|| ) v sin θ cos θ. (9.3)


Since f⊥ > f|| , the resulting net force produces a forward thrust (op-
posite to the direction of the wave velocity, see Fig. 9.4A), which in
light of Eq. 1.3 is proportional to the viscosity of the liquid. Adding
the components perpendicular to the direction of motion we obtain
a net downward pointing force that resists the upward motion of the
segment,

F “ = F ⊥ cos θ + F || sin θ = ( f⊥ cos2 θ + f|| sin2 θ)v. (9.4)


Repeating the above exercise for the down-moving segment in
Fig. 9.4B, it is easy to see that the net force on it parallel to the
direction of motion again points to the right and is equal to F ’ in
Eq. 9.3. (Since both v and θ now change sign in Eq. 9.3 the direction
of the net thrust does not change). The net force perpendicular to
the direction of motion does change sign and is F ‘ = ’F “ , the latter
being given in Eq. 9.4.
A similar analysis can be carried out for each segment along the
¬‚agellar rod. The net outcome is that, because of the shape of the ¬‚a-
gellum, hydrodynamic forces alone are capable of propelling the
sperm along a steady direction towards its target, the egg. (Note that if
there is an integral number of wavelengths along the ¬‚agellum then,

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