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CELL INDEX

Fig. 3.8 Cell-lineage diagram generated from a simulation of cell dynamics in the
model of Kaneko and Yomo. The system simulated contains more chemical components
than the one described in the text, but otherwise has similar features. Each cell in the
¬nal population is assigned a subscript number (its index i ; see Fig. 3.7). The
differentiation of cells is plotted with time along the vertical axis. In this diagram, each
branch point corresponds to a cell division, while the color indicates the cell type.
(Reprinted from Furusawa and Kaneko, 1998, with permission from Elsevier
publishers.)



(iv) The hierarchical structure appears gradually. Up to a certain
number of cells (which depends on the model parameters),
all cells have the same biochemical state (i.e., xiA (t), xiB (t), and
xiS (t) are independent of i) (Fig. 3.9A). When the total num-
ber of cells rises above a certain threshold value, the state
with identical cells is no longer stable. For example, the syn-
chrony of biochemical oscillations in different cells of the
cluster may break down (by the phases of xiA (t), xiB (t), xiS (t) be-
coming dependent on i). Ultimately, the population splits
into a few groups (˜˜dynamical clusters”), the phase of the
oscillator in each group being offset from that in other
groups, like groups of identical clocks in different time zones
(Fig 3.9B).
(v) When the ratio of the number of cells in the distinct clusters
falls within some range (depending on model parameters),
3 CELL STATES: STABILITY, OSCILLATION, DIFFERENTIATION 75




A B
Chemical 3 Chemical 3




Chemical 2
Chemical 2



Chemical 1
Chemical 1




C D Chemical 3
Chemical 3




Chemical 2 Chemical 2



Chemical 1 Chemical 1

Fig. 3.9 Schematic representation of the differentiation scenario in the isologous
diversi¬cation model of Kaneko and Yomo. When there are N cells and C chemicals, the
state space of the multicellular system is NC-dimensional. The three axes in the ¬gure
represent the state of an individual cell in the multicellular system for C = 3. A point in
this three-dimensional space corresponds to a set of instantaneous values of the three
chemicals. As long as the biochemical states of the replicating cells are identical, a point
along the orbit could characterize the synchronous states of each cell. This is illustrated
in panel A, where the four circles, representing cells with the same phase and magnitude
of their chemicals, overlap. With further replication, cells with differing biochemical
states appear. First, chemicals in different cells differ only in their phases; thus the circles
in panel B still fall on the same orbit, albeit well separated in space. With further
increase in cell number, differentiation takes place: not only the phases but also the
magnitudes (i.e., the averages over the cell cycle) of the chemicals in different cells will
differ. The two orbits in panel C represent two distinct cell types, each different from the
original cell type shown in panels A and B. Panel D illustrates the “breeding true” of the
differentiated cells. After the formation of distinct cell types, the chemical compositions
of each group are inherited by their daughter cells. That is, the chemical compositions of
cells are recursive over subsequent divisions, as the result of stabilizing interactions. Cell
division is represented here by an arrow from a progenitor cell to its progeny. (Adapted,
with changes, from Kaneko, 2003.)


the differences in intracellular biochemical dynamics are mu-
tually stabilized by cell--cell interactions.
(vi) With further increase in cell number, the average concentra-
tions of the chemicals over the cell cycle become different.
That is to say, groups of cells come to differ not only in the
phases of the same biochemical oscillations but also in their
76 BIOLOGICAL PHYSICS OF THE DEVELOPING EMBRYO


average chemical composition integrated over the entire life-
times of the cells (Fig. 3.9C). After the formation of cell types,
the chemical compositions of each group are inherited by
their daughter cells (Fig. 3.9D).
The addition of ¬‚uctuating terms (representing the random ¬‚uctua-
tions inherent in biological systems) to the rate equations, Eqs. 3.8
and 3.9, does not change the above developmental scenario, which is
therefore robust.
In contrast to the Keller model described earlier, in which differ-
ent cell types represent a choice among basins of attraction for a
multi-attractor system, external in¬‚uences having the potential to
bias such preset alternatives, in the Kaneko--Yomo model interactions
between cells can give rise to stable intracellular states that would
not exist without such interactions. Isologous diversi¬cation thus
provides a plausible model for the community effect (Gurdon, 1988),
described above. It is reasonable to expect that both the intrinsic mul-
tistability of a dynamical system of the sort analyzed by Keller as well
as the interaction-dependent multistability of other such systems, as
described by Kaneko, Yomo, and coworkers, are utilized in initiating
developmental decisions in various contexts in different organisms.


Perspective
Living cells are immensely complex, multicomponent, entities, which
are subject, in principle, to random ¬‚uctuations and chaotic behav-
ior. Despite such complications, important cellular subsystems act as
well-behaved dynamical systems. The physical laws governing such
systems ensure that the concentrations of key regulatory molecules
that trigger important events in the early embryonic cell cycle un-
dergo regular, self-organizing temporal variations. It is plausible that
alternative, stable, biochemical states, intrinsic to the individual cell
or dependent on interactions between cells, are utilized in adding
layers of control (in terms of regulated checkpoints) to the mature
cell cycle and initiating pathways of cell diversi¬cation -- determi-
nation and differentiation -- during subsequent development. Many
processes of embryogenesis discussed in this book from this point
onward are based on the existence and action of cellular mecha-
nisms of oscillatory and multistable behaviors. Although such mech-
anisms are inevitably complex, and interconnect with other subcel-
lular mechanisms, their underlying physical bases (and evolutionary
origins) are likely to be the kind of generic dynamical systems dis-
cussed in this chapter.
Chapter 4


Cell adhesion,
compartmentalization,
and lumen formation

In Chapter 2 we followed development up to the ¬rst nontrivial mani-
festation of multicellularity, the appearance of the blastula. To de-
scribe the mechanism of blastula formation we needed a model for
cleavage, as well as for the collective behavior of a large number of
cells in contact with one another. We based our model on physical pa-
rameters such as surface tension, cellular elasticity, viscosity, etc. and
when possible related these quantities to experimentally known infor-
mation such as the expression of particular genes. However, we have
so far not dealt with the fundamental question concerning multicel-
lularity: what holds the cells of a multicellular organism together?
As cells differentiate (see Chapter 3) they become biochemically
and structurally specialized and capable of forming multicellular
structures, with characteristic shapes, such as spheroidal blastu-
lae, multilayered gastrulae, planar epithelia, hollow ducts or crypts.
The appearance and function of these specialized structures re¬‚ect,
among other things, differences in the ability of cells to adhere to
each other and the distinct mechanisms by which they do so. Dur-
ing development certain cell populations need to bind, to varying
extents, to some of their neighbors but not to others. In mature tis-
sues the nature of the cell--cell adhesion contributes to their func-
tionality: the manner in which two cells bind tightly to one another
in the epithelial sheet lining the gut, for example, must be differ-
ent from the looser attachment between the endothelial cells lining
blood vessels. Differentiated and differentiating cells must therefore
possess distinct adhesion molecules and apparatuses that re¬‚ect bio-
logical speci¬city. But cell adhesion also has common features across
cell types and classes of adhesion molecules, and these can often be
studied by physical methods and theories.
The major classes of cell adhesion molecules include the cal-
cium dependent cadherins (Takeichi, 1991, 1995; Gumbiner, 1996;
Wheelock and Johnson, 2003), the immunoglobulin superfamily (which
also includes antibodies) an example of which is N-CAM (Williams and
Barclay, 1988; Hunkapiller and Hood, 1989), the selectins (Bevilacqua
et al., 1991), and the integrins (Hynes, 1987; Hynes and Lander, 1992).
The molecules in the ¬rst three classes are primarily responsible for
78 BIOLOGICAL PHYSICS OF THE DEVELOPING EMBRYO


direct cell--cell adhesion and are called cell adhesion molecules or
CAMs. Cadherins, for example, enter into homophilic interactions in
which a molecule on one cell binds to an identical molecule on a
second cell. Integrins mainly mediate cell-extracellular-matrix (ECM)
interactions and are called substratum adhesion molecules or SAMs.
All CAMs and SAMs have distinct structures and specialized morpho-
genetic roles (Edelman, 1992).
The formation of complex multicellular structures is determined
not only by the chemical nature of the cells™ adhesion molecules but
also by the distribution of these molecules on the cell surface. Epi-
thelial cells forming strictly two-dimensional sheets must have pre-
dominantly CAMs along their lateral surfaces, whereas SAMs must
populate their basal surfaces, along which interaction with the sup-
porting specialized extracellular matrix, the basal lamina, occurs
(Fig. 4.1). Such a distribution of CAMs and SAMs renders epithelial
cells polarized.


Adhesion and differential adhesion in development
Adhesion enters into the phenomena of embryonic development in
several distinct ways. The ¬rst, and most straightforward, way is in
simply holding tissues together. This, of course, is the default role
of cell--cell adhesion in all tissues, embryonic or adult. Mature tis-
sues contain the de¬nitive, relatively long-lived forms of the CAM-
containing junctions represented in Fig. 4.1. These comprise desmo-
somes and adherens junctions, hemidesmosomes and focal adhesion
complexes, as well as tight junctions, which provide a transepithelial
seal impermeable to ions and polar molecules, and gap junctions,
which allow ions and other small molecules to pass directly from
one cell to another (Alberts et al., 2002). During early development
the CAM-containing junctions are present in apparently immature
forms (DeMarais and Moon, 1992; Kofron et al., 1997, 2002; Eshkind
et al., 2002) consistent with the provisional arrangement of cells and
their capacity to rearrange during this period.
The other roles for adhesion during development are based on its
modulation -- the phenomenon of differential adhesion. As we will see in
this and following chapters, the regulated spatiotemporal modulation
of adhesion is an important driving force for major morphogenetic
transitions during embryogenesis. The simplest form of this is the de-
tachment of cell populations from existing tissues. This is usually a
prologue to their relocation, as in gastrulation and the formation of
the neural crest (see Chapters 5 and 6). But the modulation of adhe-
sive strength without complete detachment also has morphogenetic
consequences, whether it occurs locally, on the scale of the individual
cell surface, or more globally, on the scale of groups of cells within
a common tissue.
The polar expression of CAMs can lead directly to morphogenetic
change, as illustrated in Fig. 4.2. In the process of differentiation some
4 CELL ADHESION, COMPARTMENTALIZATION, AND LUMEN FORMATION 79



JUNCTIONAL ADHESIONS NON-JUNCTIONAL ADHESIONS


Apical
cell surface Glycocalyx


Tight junction
CELL-TO-CELL




Adhesion belt
Cadherins


Desmosome IgG-like CAMs

Integrins
Selectins
Gap junction


Focal contact
CELL-TO-MATRIX




Basal cell
surface
Extracellular matrix

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