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Chapter 6 (Zeng et al., 2003), obtained the three-dimensional develop-
mental time series of successive stages of limb skeletogenesis shown
in Fig 8.15C.

During the later stages of embryogenesis the body as a whole becomes
more structurally complex and functionally integrated. This means
that basic physical mechanisms become correspondingly less applica-
ble to an understanding of the changes in the shape and form of the
entire organism as development proceeds. At the same time, newly
arising subdomains of the developing organism, the cell clusters that
constitute the organ primordia, now become the loci for many of
the same physical processes discussed in earlier chapters as determi-
nants of body form. These include the viscoelastic behavior of epi-
thelia and mesenchyme, differential adhesion, cell-state transitions
based on multistable transcription-factor networks, and juxtacrine,
paracrine, and reaction--diffusion-based pattern-forming systems. The
organs serve the body but are also partially independent of it. They
are therefore subject to some architectural constraints different from
those of body plans. Their functions -- transport in the case of the
vascular system, secretion for the salivary glands, locomotion and
grasping for the limbs, for example -- are best accomplished by mod-
ular, tubular, or branched structures. Unconstrained by the need to
produce an integral body, physical (in concert with genetic) mecha-
nisms of differentiation, morphogenesis, and pattern formation, act-
ing on the epithelial and mesenchymal components characteristic of
the advanced, rather than the early, stages of embryogenesis, mobi-
lize genetic processes and products to generate the elaborate organs of
complex organisms.
Chapter 9

Fertilization: generating
one living dynamical system
from two

So far we have followed early development from the ¬rst cleavage
of the zygote (fertilized egg) to the appearance of fully developed
organs. We have reviewed the biology of the most fundamental pro-
cesses along this path, introduced relevant physical concepts, and
used them to build models of the same processes. As the organism ma-
tures it eventually arrives at the stage where it is ready to reproduce.
At this point the female and the male possess the fully developed sex
cells or gametes (i.e., egg and sperm), the fusion of which, termed
fertilization, sets the developmental process in motion. Fertilization
thus can be viewed both as an end and a beginning, the process that
simultaneously terminates and initiates the developmental cycle.
The major activities during fertilization that apply generally to
any sexually reproducing organism are: (i) contact and recognition
between the sperm and the egg; (ii) the regulation of sperm entry
into the egg; (iii) fusion of the sperm™s and egg™s genetic material;
and (iv) activation of the zygotic metabolism.
It is clear from this list that fertilization is among the most com-
plicated and spectacular of all developmental processes. It must also
be clear that highly sophisticated machinery is needed to carry out
the tasks associated with fertilization. The sperm must often travel
over great distances relative to its size, it must distinguish between
eggs of different related species (in certain marine organisms, sea
urchins and abalone for example). Upon encountering the sperm, the
egg undergoes a series of changes that alter the electrical (in some
species) and mechanical properties of its membrane in order to pre-
vent multiple fertilization (˜˜polyspermy”). Next, the zygote propagates
a series of traveling chemical waves followed by a set of mechanical
waves -- rippling changes in contractility in the egg cortex -- that even-
tually lead to cleavage. How can physics help to unravel these mys-
teries? Obviously we cannot attempt to construct a physical model of
the full process of fertilization. Instead, we will concentrate on those
details that clearly require physical mechanisms for their enaction. In
particular, we will consider sperm locomotion in a viscous medium,
the electrical phenomena associated with egg membrane potential
that control sperm entry, the propagation of calcium waves in the

egg cytoplasm upon sperm entry, and initiation of the contractile
waves in the egg cortex that are the prelude to cleavage. Most of the
physics that we will need has already been introduced; the rest will
be discussed along the way.

Development of the egg and sperm
The egg and sperm each represent the endpoints of a complex de-
velopmental process. In the case of the gametes, or sex cells, this
process is referred to as gametogenesis. In contrast with the processes
of organogenesis described in Chapter 8, in which the functional end-
points were units consisting of many cells, and typically many types
of cells, gametogenesis gives rise to specialized cells that function in-
dividually and at a great distance from their sites of differentiation
in the ovaries and testes (collectively, the gonads).
In most sexually reproducing organisms, including insect and ver-
tebrate species, the ˜˜germ” cells, which develop into the sperm and
eggs, do not even originate in the gonads. They begin their life as a
distinct spatially sequestered cell lineage (the ˜˜germ line”) early in
embryogenesis, during blastula formation. The fate of these cells is
¬xed by the incorporation into their cytoplasm (the ˜˜germ plasm”)
of a set of molecular determinants during cleavage. The germ cells
of the developing organism are thus among the earliest cell types to
be determined during embryogenesis (De Felici, 2000; Starz-Gaiano
and Lehmann, 2001). As with other types of cell differentiation, gam-
etogenesis requires extensive remodeling of chromatin (Kimmins and
Sassone-Corsi, 2005).
Germ cells are a migratory population, much like the neural crest
cells discussed in Chapter 5. The earliest cells to arise in the germ
line, the primordial germ cells, or PGCs, constitute a mesenchymal
population that gets conveyed to the gonads by one of several differ-
ent routes, depending on the species. In frogs and toads the PGCs are
¬rst identi¬able as a group of cells lining the ¬‚oor of the blastocoel.
They become concentrated in the posterior region of the larval gut
and migrate along the dorsal side of the gut, then along the tissue
connecting the gut to the inner surface of the abdominal wall (the
˜˜dorsal mesentery”), and ¬nally into the gonadal mesoderm (Gilbert,
In mammals, PGCs arise in a region of the epiblast of the gastrulat-
ing embryo that becomes extra-embryonic mesoderm i.e., the support-
ive tissues outside the developing body (Ginsburg et al., 1990); and
then have to ¬nd their way into the body and ultimately the gonads.
They ¬rst accumulate in the allantois (a sac that develops from the
posterior portion of the developing digestive tube), then move into
the yolk sac, the membranous pouch beneath developing mammalian
embryos that is also the source of blood-forming stem cells. They then
move through the posterior- or hindgut, up the dorsal mesentery, and
into the developing gonads.

Primordial germ cells typically move as cell clusters, like the neu-
ral crest (Gomperts et al., 1994), but they may also move as individ-
ual cells (Weidinger et al., 2002). Xenopus PGCs move by extending a
¬lopodium into which cytoplasm streams, and then they retract this
˜˜tail” (Wylie and Heasman, 1993). They appear to be guided by hapto-
tactic cues from the surrounding ECM. However, the PGCs of another
frog, Rana, (Subtelny and Penkala, 1984) and those of some species
of ¬sh (Braat et al., 1999) appear to translocate by a ˜˜passive” mech-
anism that does not utilize individual cell motility, as has also been
suggested for neural crest dispersion (see Chapter 6).
Once the organism reaches sexual maturity, the immature germ
line cells (termed, at this stage, oogonia and spermatogonia) resident
in the gonads begin differentiating into eggs and sperm. For many
species, however, gametogenesis is not completed in the gonads. In
mammals, the sperm, even after it is fully formed, must enter the
female reproductive tract before it is ˜˜capacitated” (physiologically
capable of fertilizing the egg), and the oocyte (the immature egg) does
not even complete meiosis (reduction of its chromosome number to
the haploid state, see Chapter 3 and below), until it is fertilized.
Meiosis, like capacitation, is one of the important steps, some of
which are in common and some distinctive, that oogonia and sper-
matogonia (˜˜gonial cells”) must take in order to give rise to de¬nitive
eggs and sperm. These steps are referred to as oogenesis and spermatoge-
nesis respectively. Before meiosis occurs, the gonial cells must undergo
a series of maturation steps associated with cell division that leads
to a population of oocytes or spermatocytes (immature sperm). Recall
from earlier discussions (Chapters 2 and 3) that the typical cell in a
diploid organism (sea urchins, fruit ¬‚ies, amphibian, mammals, and
so forth) by de¬nition contains two versions, maternal and paternal,
of each chromosome. Like any other cell division, the ¬rst meiotic di-
vision, meiosis I, is preceded by DNA synthesis, yielding two attached
copies, the ˜˜sister chromatids,” of each of the two chromosome ver-
sions. During the metaphase of meiosis I the corresponding versions
of the chromosomes, the ˜˜homologs,” line up with one another, an
event referred to as ˜˜synapsis” that only happens in cells undergo-
ing meiosis (Fig. 9.1). When this division occurs, therefore, it is the
homologs that are partitioned to the daughter cells, not the sister
chromatids as in normal (mitotic) cell division (see Fig. 2.1). Since
haploid daughter cells containing only one version of each chromo-
some are produced from the diploid mother cell, meiosis I (Fig 9.1,
middle panel) is referred to as a ˜˜reduction division.” Meiosis II fol-
lows (bottom panel), but this is similar to a mitotic division; the sister
chromatids are partitioned to the daughter cell, the end result being
a set of haploid cells.
Each initial oocyte or spermatocyte thus gives rise to four progeny
cells. One important difference between the egg- and sperm-forming
processes in many types of organism, ranging from insects to mam-
mals, is that whereas all four progeny of spermatogenesis are func-
tioning sperm, only one of the four meiotic products of oogenesis is





Metaphase I
MEIOSIS I (reductional division)


Anaphase I

Telophase I
MEIOSIS II (equational division)

Metaphase II

first polar body


polar bodies

Fig. 9.1 The stages of meiosis. Spermatogonia and oogonia (collectively, “gonial cells”),
the diploid cells that are committed to form the male and female gametes, i.e., the sperm
and egg, are distinct cell types arising respectively in the testes and ovaries. Their mitotic
progeny, the primary spermatocyte and primary oocyte, undergo a process of reduction
division or meiosis (see the main text) in order to give rise to the haploid gametes. The
early stages of meiosis are similar in the male and female lineages. Prophase I (top panel)
is divided into several steps. In leptotene, the chromosomes assume an extended
con¬guration. (Two homologous pairs of chromosomes are shown; the red pair is
descended from chromosomes contributed by the maternal parent and the blue pair
from chromosomes contributed by the paternal parent in the fertilization event that gave
rise to the individual in which the pictured meiosis is occurring). Each of these
chromosomes has already been replicated during the S-phase (not shown) that precedes
prophase I. During zygotene, the homologs undergo pairing (synapsis), so that the
corresponding chromosomes of maternal and paternal origin are physically linked to
each other. These linked pairs are called “bivalents.” At pachytene, the chromosomes
become shorter and thicker and the two sister chromatids of each chromosome begin

a functioning egg. The meiotic divisions leading to egg formation
are highly asymmetric, re¬‚ecting the requirement on the egg to
have large stores of cytoplasmic materials -- nutrient yolk, protein-
encoding, ribosomal, and transfer RNAs, localized morphogenetic fac-
tors, cell-cycle regulatory proteins -- to support the early stages of de-
velopment (see Chapter 3). Meiosis I and II thus each produce small
nonfunctional cells (the ¬rst and second ˜˜polar bodies”) in addition to
the oocyte, which receives almost all the cytoplasm. As noted above,
meiosis II does not occur until after fertilization in mammalian eggs.
Meiosis in both egg and sperm is followed by further matura-
tional steps and here, in all species, the steps are quite different for
the female and male gametes (McLaren, 1984; McKim et al., 2002;
Giansanti et al., 2001). In both cases differentiation is typically aided
by accessory cells. In oogenesis, cells of the same oogonial lineage as
the oocyte, ˜˜nurse cells,” and supporting cells of the ovary, ˜˜follicle
cells,” play distinct but equally essential roles (Gosden et al., 1997). In
spermatogenesis, all cells of the spermatogonial lineage typically give
rise to gametes. As a result of the activities of germ-line and maternal
accessory cells the prefertilization oocyte typically expands greatly in


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