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vary in time (Eq. B1.1a, vx ≈ x/ t). This is often used as the criterion
distinguishing solids from liquids. (For a mathematically more formal
discussion of various deformations arising in biological materials see
Fung, 1993 or Howard, 2001.)
The most conspicuous property of a spring (or any perfectly elastic
material) is that upon the action of a force it adapts instantaneously
via deformation: as soon as F is applied the displacement x in
Eq. 1.6 is established. As we have seen, in the viscous regime a shearing
force determines the rate of deformation rather than the deformation
itself. The prototype of such behavior is a piston moving in oil: more
force needs to be applied to move the piston faster.
There exists a large class of materials, including most cells and
tissues, which exhibit both elastic and viscous properties; such mate-
rials are termed viscoelastic. When a viscoelastic material is deformed,
on a short time scale it behaves mostly as an elastic body whereas on
a longer time scale it manifests viscous liquid characteristics. When
a piece of tissue is compressed with a constant force, the resulting
deformation (i.e., strain) shows a characteristic time dependence: the
tissue ¬rst quickly shrinks in the direction of the force (just as a
spring would), but the ¬nal deformation is reached through a slow
¬‚ow. Alternatively, if one imposes a de¬nite deformation on a vis-
coelastic material, the resulting stress varies in time until a ¬nal
equilibrium state is reached.
The mathematical description of viscoelasticity is rather compli-
cated. We will deal with it, in a somewhat simpli¬ed manner, later,
where it is relevant to understanding certain developmental phenom-
ena. (For a comprehensive discussion of viscoelasticity in biological
materials, see Fung, 1993).

Basic, ˜˜generic” physical mechanisms can provide insight into many
processes that occur within and between living cells. It is essential to
recognize, however, that neither cytoplasm nor multicellular aggre-
gates are the sort of ˜˜ideal” materials that physics excels in describ-
ing. Each cellular and tissue property will be, in general, a result of

many superimposed physical properties. Thus any standard physical
quantity (e.g., a diffusion coef¬cient, an elastic modulus) will have
a more restrictive meaning and the temporal and spatial range of
any simple physical law will be limited. As we have seen, however, it
is possible to build a certain amount of complexity into a physical
representation and come closer to capturing biological reality. This
can be achieved by de¬ning ˜˜effective” physical parameters, which
incorporate the complexity of the biological system, and using them
in the same equations and relationships that their standard coun-
terparts obey. Typically, the validity of such equations cannot be de-
duced from ¬rst principles and must be checked experimentally. The
effectiveness of studying living systems using physics, therefore, will
often lie in establishing analogies rather than equivalences between
complex biological phenomena and well-understood processes in the
inanimate world.
Chapter 2

Cleavage and blastula

In the previous chapter we saw how the simple physical assumption
that the cell is a droplet of liquid comes into con¬‚ict with experi-
mental evidence when the transport of molecules in its interior or
the response of an individual cell to mechanical stress are considered.
By adding more physics to the default concept of diffusion (external
forces, viscosity, elasticity) we were able to approach the biological
reality of cell behavior more closely. This analysis also had the pre-
mium of helping us to identify levels of organization (e.g., chemotaxis
in a colony of bacteria or amoebae) at which physical laws that are
too simple to explain individual cell behavior may nonetheless be
In this chapter we will describe the transition made by a develop-
ing embryo from the zygotic, or single-cell, stage to the multicellu-
lar aggregate known as the blastula. Here again the simplest physical
model for both the zygote and the early multicellular embryo that
arises from it is a liquid drop. As in the examples in Chapter 1 our
understanding of real developing systems will be informed by an ex-
ploration of how they conform with, and how they deviate from, the
basic physical picture.

The cell biology of early cleavage and
blastula formation
The blastula arises by a process of sequential subdivision of the zygote,
referred to as cleavage. Cleavage, in turn, is a variation on the process
of cell division that gives rise to all cells. In cell division both the
genetic material and the cytoplasm are apportioned between the two
˜˜daughter” cells. To ensure that the resulting cells are genetically
identical to their progenitor, the DNA (essentially all contained in
the cell™s nucleus) must be replicated before division. A duplicate set
of DNA molecules is thus synthesized in the nucleus, well before the
cell exhibits any evidence of dividing into two; it will do this using
the separated strands of the original double helix as templates.

The cell™s DNA is complexed with numerous proteins, forming a
collection of ¬bers known as chromatin. Although the chromatin ¬bers
form a dense tangle when the nucleus is intact, each ¬ber is actually
a separate structure, a chromosome. In the organisms that we are con-
sidering in this book (˜˜diploid” organisms), all the cells of the embryo
and the mature body, except the egg and sperm and their immediate
precursors, contain two distinct versions of each chromosome, one
contributed by each parent during fertilization (see Chapter 9). Thus
a human cell contains 23 pairs, or 46 chromosomes.
Just before the cell divides the nuclear envelope (the membranes
and underlying proteinaceous layer enclosing the nucleus) disassem-
bles, while the chromosomes separately consolidate and can now be
visualized in the cytoplasm as the individual structures they actually
are. Since DNA synthesis has occurred by this time, there are two
identical copies of each chromosome, referred to as sister chromatids,
still attached to each other by means of a structure called a centromere,
which contains a molecular glue (the protein cohesin). Human diploid
cells at this stage contain 46 pairs of such sister chromatids.
At this point a series of changes takes place that lead to: (i) the
separation of sister chromatids; (ii) the two resulting sets of chromo-
somes being brought to opposite ends of the cell (˜˜mitosis”); and (iii)
the cytoplasm and surrounding plasma membrane of the cell dividing
into two equal portions (˜˜cytokinesis”). Mitosis is guided by a piece
of molecular machinery known as the mitotic apparatus or spindle,
made up of protein ¬laments called microtubules and microtubule-
organizing centers known as centrosomes, located at opposite sides of
the cell and forming the poles of the spindle (Fig. 2.1). Immediately be-
fore mitosis takes place a single centrosome, located near the nucleus,
separates into two, which, upon assuming their polar locations, ex-
tend long microtubules. These microtubules (the same number from
each centrosome) either attach to a portion of each of the two chro-
mosomes of the sister chromatids (the kinetochore) or form asters, star-
like arrays of shorter microtubules. The spindle employs molecular
motor proteins, such as microtubule-associated dynein and the BimC
family of kinesin-like proteins located in the centrosomes, to exert
tension on the kinetochores and to separate the sister chromatids
(Nicklas and Koch, 1969; Dewar et al., 2004).
Cytokinesis is regulated by another class of cytoskeletal ¬laments,
composed of the protein actin as well as additional molecular mo-
tor molecules such as kinesin. Actin-containing micro¬laments form
a contractile ring beneath the cell surface and, in association with
the molecular motors, cause the formation of a groove or furrow
between the two incipient daughter cells that eventually pinches
the cells apart. Once cell division is completed the chromosomes re-
arrange themselves into a ball of chromatin around which the nu-
clear envelope reforms.
The processes just described are collectively known as the ˜˜cell
cycle,” which is schematized into four discrete phases: M (mitosis,
including cytokinesis), G1 (time gap 1), S (DNA synthesis), and G2


Sister chromatids




Fig. 2.1 The cell division cycle. The cell spends most of its lifetime in the interphase
state, during which period its intact nucleus contains the full set of chromosomes in the
form of the tangled DNA“protein complex called chromatin. If the cell divides then its
DNA is replicated and its centrosome is duplicated during interphase. In the division of
typical somatic cells (as pictured) the cell size also increases during interphase, but for
cleavage divisions (see Fig. 2.2) cell size remains constant. Cell division is accomplished
by mitosis (A“F). At prophase (A), the asters (blue microtubules) assemble at the two
centrosomes (small blue boxes), which have moved away from one another. Inside the
nucleus the replicated chromosomes, each consisting of two attached sister chromatids,
condense into compact structures. For illustrative purposes two chromosomes are
pictured here; diploid cells have two copies of each of several chromosomes. At the
beginning of prometaphase (B), the nuclear envelope breaks down abruptly. The spindle
then forms from the microtubules that extend from the centrosomes and attach to the
kinetochores of the chromosomes. The chromosomes then begin to move toward the
cell equator, de¬ned by the location of the centrosomes, which are now at opposite
poles of the cell. At metaphase (C), the chromosomes are aligned at the equator and
sister chromatids are attached by microtubules to the opposite spindle poles. At
anaphase A (D), the sister chromatids separate to form daughter chromosomes. By a
combination of shortening of the kinetochore microtubules and further separation of
the spindle poles, the daughter chromosomes move toward opposite ends of the cell. At
anaphase B (E), the chromosomes are maximally separated and a micro¬lament-
containing contractile ring begins to form around the cell equator. At telophase (F), the
chromosomes decondense and a new nuclear envelope forms around each of the two
complete sets. The contractile ring deepens into a furrow, which, as cytokinesis
proceeds, pinches the dividing cell into two daughters.

(time gap 2). The latter three collectively form the interphase (Fig. 2.1).
For most cells M lasts less than an hour and S one to several hours,
depending on the genome size. The two gap phases G1 and G2 are per-
iods in which various synthetic processes take place, including those
in preparation for the events during the M and S phases. Since the

activities in G1 and G2 are keyed to the requirements of different cell
types, their durations vary widely. Cleavage-stage embryos typically
utilize molecules that have been synthesized and stored during the
process of egg construction or oogenesis, and therefore have G phases
that are brief or nonexistent.
DNA synthesis, mitosis, and cytokinesis are unique events in the
life of any cell, but considered in the continuity of cellular life they
are periodic processes. As such, it would be natural for them to be
controlled by molecular clocks, and indeed several such regulatory
clocks exist in dividing cells. Molecular clocks that regulate entry
into DNA synthesis and mitosis are based on temporal oscillations of
the concentrations of members of the cyclin family of proteins. Such
oscillations are the physical consequences of positive and negative
feedback effects in dynamical systems, such as that represented by
the cell™s biochemistry, and will be discussed in the following chapter.
The control of cytokinesis is less well understood.
In contrast with the cell division that occurs later in embryogen-
esis and in the tissues of growing and mature organisms, which (like
the cell division of free-living cells) is typically associated with a dou-
bling in cell mass, in cleavage a single large cell is subdivided with-
out increase in its mass. This has the consequence that with each
successive subdivision of the zygote the ratio of nuclear to cytoplas-
mic material increases. In the frog embryo, the ˜˜midblastula transi-
tion,” a set of molecular and cell behavioral changes leading to the
morphological reorganization of the embryo known as gastrulation
(Chapter 5), is regulated by the titration of one or more cytoplasmic
components resulting from this changing ratio (Newport and
Kirschner, 1982a, b).
The geometry and topology of the blastula, although they differ
for different types of organisms, are relatively simple (Fig. 2.2). Most
typically, the end result is a ball of cells with an interior cavity (the
˜˜blastocoel”). The ball can be of constant thickness, as in the sea
urchin or Drosophila (fruit ¬‚y) embryo, where it is a single layer of
cells called the blastoderm (˜˜cell skin”). In amphibians, such as the
frog, the ball is of nonuniform thickness as a result of different rates
of cleavage at opposite poles of the zygote. In mammals, such as the
mouse and human, the outer surface of the ball consists of a layer
of ¬‚at cells (the ˜˜trophoblast”), which gives rise to the extraembry-
onic membranes that attach to and communicate with the mother™s
uterus. A cluster of about 30 cells termed the ˜˜inner cell mass,” which
forms at one pole of the trophoblast™s inner surface, gives rise to the
embryonic body. In certain cases, such as in species of mollusks that
develop from large eggs, the ball of cells develops with no interior
cavity (Boring, 1989). This is called a ˜˜steroblastula” (solid blastula).
The routes by which the blastula takes form also vary in differ-
ent groups of organisms. While cleavage can be a symmetrical pro-
cess over multiple division cycles, the sizes of the cells resulting from
cleavage are often unequal. The reason is that the zygote typically has
within its cytoplasm, stored in a spatially nonuniform fashion, ma-
terials provided to the egg by the mother™s tissues during oogenesis.



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