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between cells over a distance of approximately 40 cell bodies (light grey). This situation
mimics the Dpp gradient in the wing imaginal discs of the Drosophila larvae. The middle
panel illustrates the proposed mechanism of gradient generation: morphogen molecules
emanating from a linear source encounter and bind to a homogeneous distribution of
receptors (R) in the adjacent two-dimensional space. On the right, this situation is
simpli¬ed to a one-dimensional model with constant morphogen production at x = 0,
absorption at x = x max , and an initially uniform receptor concentration throughout.
(Reprinted from Lander et al., 2002, with permission from Elsevier.)

3. If R tot is the total number of receptor molecules per cell and A
and B are, respectively, the fractional (normalized to R tot ) concentra-
tion of free and receptor-bound morphogens, then the evolution of
the morphogen pattern (subject to the above conditions) is governed
by the following equations:
‚A ‚2 A
= D 2 ’ kon R tot A(1 ’ B ) + koff B , (7.8a)
‚t ‚x
= kon R tot A(1 ’ B ) ’ koff B ’ kdeg B . (7.8b)
In the most general reaction--diffusion systems (cf. Eq. 7.7) every
molecular species is capable of diffusing (see also below). But since
the diffusive term is missing in Eq. 7.8b, the above equations rep-
resent a special type of reaction--diffusion system, in which freely
diffusing molecules (i.e., morphogens) react with immobilized ones
(i.e., receptors). All the parameters in the above equations, including
the morphogen diffusion coef¬cient D, can be estimated reasonably
accurately from experimental data.
4. For parameter values compatible with the experimental results,
biologically ˜˜useful” situations with steady-state gradients of recep-
tor occupancy are generated by the system de¬ned by Eqs. 7.8a, b. For
the gradient to be biologically useful it must be able to distribute
spatial information over the entire ¬eld of cells and thus not be too
steep. One situation is illustrated in Fig. 7.8A, where the solution of
Eqs. 7.8a, b for B is plotted for a particular set of model parameters
(see ¬gure legend). This solution is not biologically useful, since the
variation in B, and thus the ability of the morphogen to produce pat-
tern, is at any time restricted to a negligibly narrow spatial region
(i.e., the gradient is too steep). A different set of model parameters,
however, produces a morphogen gradient that is biologically useful



0.6 0.5 1.0
0.75 0.15
0 20 40 60 80 100 0 20 40 60 80 100
DISTANCE (microns) DISTANCE (microns)

Fig. 7.8 Morphogen gradients generated in the model of Lander et al. (2002).
Equations 7.8 were solved with the initial conditions (at t = 0) B = 0 for all x and A = 0
for all values of x different from zero and the boundary conditions A = B = 0 at
x = x max and a nonzero ¬‚ux, ‚ A /‚t = v /R tot , at x = 0. (A) A biologically
ineffective gradient of the fractional receptor occupancy B , for parameter values
D = 10’7 cm2 s’1 , kdeg = 2 — 10’4 s’1 , v /R tot = 5 — 10’4 s’1 , kon R tot = 1.32 s’1 ,
koff = 10’6 s’1 . (B) A biologically “useful” gradient of the fractional receptor occupancy
for the parameter values listed above, with the exception of v /R tot = 5 — 10’5 s’1 and
kon R tot = 0.01 s’1 . The time interval between successive curves is 300 s in panel A and
1800 s in panel B. The cumulative time represented by selected curves is shown in
hours. The curves in B, unlike those in A, approach steady-state receptor occupancy.
(After Lander et al., 2002.)

(Fig. 7.8B). For this choice of parameters, steady-state receptor occu-
pancy occurs in about 4 hr, and the resulting gradient extends over
the entire ¬eld. Not surprisingly, such solutions arise only when the
rate of morphogen production v is slower than receptor turnover,
v < R tot kdeg .
Further generalization of the model (allowing for ligand--receptor
complexes internalized by the cells to signal from within endocytic
compartments, followed either by their return to the cell surface or
destruction) does not change the conclusion that the extracellular
diffusion of morphogens can effectively set up gradients which can
eventually determine cell fate (Lander et al., 2002). The same study
also provided strong quantitative evidence that other mechanisms of
morphogen transport (e.g., bucket-brigade or transcytosis) would re-
quire a series of cell-biological events to occur at implausibly fast rates.
But since endocytosis plays an additional role in the long-range move-
ment of Dpp that is not addressed in the pure extracellular diffusion
model (Kruse et al., 2004), the question of how the Dpp gradient is
actually established cannot be considered to be entirely settled.
Once the gradient of a signaling molecule is established (by what-
ever means), the next step is for cells to respond to it. There are various
ways in which this can happen. The simplest way in which cells can
interpret a spatially graded signal is through unidirectional hierarchi-
cal induction (Fig. 7.1B(ii)), where the gradient serves as positional in-
formation and the cells respond to it according to a corresponding set
of internal thresholds (Wolpert, 1969). A more complex and general

way in which cells respond to a nonuniform signaling environment
is by an emergent system of positive and negative feedback interac-
tions with neighboring cells (Fig. 7.1B(ii)). In such cases the shape of
the resulting gradient need not be monotonic, as it would with sim-
ple diffusion, and achievement of the induced cell states is more of
an active process than for a positional information mechanism. Both
of these categories of gradient-response, or inductive, mechanisms
presuppose that changes in tissue geometry and topology via mor-
phogenetic mechanisms (Fig. 7.1A) occur after all new cell states have
been induced. An even more complex scenario occurs when tissue re-
shaping occurs simultaneously with the generation of new cell states,
resulting in continual rearrangement of the signaling environment
(Salazar-Ciudad and Jernvall, 2002). There are numerous examples of
such ˜˜morphodynamic” mechanisms (Salazar-Ciudad et al., 2003), but
we will not consider them here. Instead, we will conclude this chap-
ter with several examples of emergent inductive pattern formation in
the establishment of the vertebrate body plan.

Control of axis formation and left“right asymmetry
The prefertilization amphibian egg is radially symmetric about the
animal--vegetal axis. After fertilization (see Chapter 9), radial sym-
metry is broken during the ¬rst cleavage division, when the cortical
cytoplasm actively rotates 30—¦ in the direction of the animal pole
while the deeper, internal, cytoplasm, containing dense yolky cells,
remains oriented by gravity (Fig. 7.9). The site where the sperm enters

ection of rotatio
(Dorsal) (pigmented) Dir n

Sperm Cytoplasm Caudal crescent

Heavy yolk


Fig. 7.9 Cortical rotation in amphibian embryos. The egg, before (on the left), and
after (on the right) the 30—¦ postfertilization rotation of the cortical cytoplasm (medium
and light gray) relative to the inner cytoplasm (blue). The cortex rotates in such a way
that the sperm entry point moves vegetally during the ¬rst cell cycle. The gray crescent
seen in the right-hand panel is formed by the overlapping of the pigmented animal pole
cytoplasm with non-pigmented vegetal pole cytoplasm. The animal pole (AP) and vegetal
pole (VP), which is close to the future site of the Nieuwkoop center, “Prospective N.C.,”
and the prospective dorsal, ventral, rostral (anterior), and caudal (posterior) regions of
the animal are shown. (Based on Elinson and Rowning, 1988, with changes.)

has traditionally been designated as the future ventral (belly) surface
of the embryo, the opposite side as the future dorsum (back), and the
axis connecting them as the dorsal--ventral (or dorsoventral) axis.
Improved marking techniques that permit the following of indi-
vidual cells and their progeny in living embryos (Lane and Smith,
1999; Lane and Sheets, 2000) have led to revisions of earlier estab-
lished Xenopus ˜˜fate maps.” (A fate map is an assignment of the cells
of an experimentally unperturbed early embryo, e.g., a blastula or gas-
trula, to the regions or speci¬c cells of the fully developed organism to
which they will give rise). In particular, it was suggested that the long-
standing designation of the dorsoventral axis contained serious incon-
sistencies. This, in turn, led Lane and Sheets (2002) to rede¬ne the
principal axes in the Xenopus embryo. They proposed to reassign the
dorsoventral axis to the animal--vegetal aspect of the embryo. The tra-
ditional dorsoventral axis is now designated as the rostrocaudal (nose
to tail) or anteroposterior axis (Figs. 7.9 and 7.10; see also Kumano
and Smith, 2002, and Gerhart, 2002). This reassignment of axes har-
monises the terminology used to describe Xenopus development with
that for other vertebrates. In particular, the assignment of the rostro-
caudal axis is now consistent with the general head-to-tail develop-
ment of vertebrate embryos. The Lane and Sheets designation of the
axes is used in Figs 7.9 and 7.10 and in the following description.
The postfertilization differential cytoplasmic rotation creates a re-
gion on the side of the embryo opposite to the sperm entry point
(i.e., the rostral side, see Fig. 7.9) called the ˜˜gray crescent.” Next
to this region gastrulation will be initiated, by the formation of an
indentation, the ˜˜blastopore,” through which the surrounding cells
Spemann and Mangold (1924) discovered that the rostral blasto-
pore lip (containing cells derived from the gray crescent) constitutes
an organizer, a population of cells that directs the movement of other
cells. The action of the Spemann--Mangold organizer ultimately leads
to convergent extension, the formation of the notochord, and thus
the body axis (see Chapter 5). When they transplanted an organizer
from another gastrula into an embryo at a point some distance from
the embryo™s own organizer, Spemann and Mangold observed that two
axes formed, resulting in conjoined twins. Since then other classes of
vertebrates have been found to have similarly acting organizers.
A property shared by organizers in other developing systems (in-
cluding invertebrates such as Hydra, one of the systems in which the
organizer phenomenon was ¬rst identi¬ed; Browne, 1909) is that if an
organizer is extirpated then adjacent cells differentiate into organizer
cells and assume its role. This suggests that one of the functions of
the organizer is to suppress nearby cells with similar potential from
exercising it. This implies that the body axis is a ˜˜self-organizing”
system. Another manifestation of self-organization is that if animal
and vegetal cells from a Xenopus embryo are dissociated, separately re-
aggregated, and confronted with each other as amorphous cell masses
then not only mesodermal tissue (see the section on mesoderm


Caudal Rostral






Fig. 7.10 Fate map of a Xenopus embryo at the late blastula stage. By this stage the
three germ layers are already determined, the mesoderm (shown as an annulus) arising
from the cells of the equatorial or marginal zone. The blastula is viewed from its left, as
is the tadpole (larval stage frog) into which it will develop. During gastrulation the
mesoderm undergoes inversion (curved arrow), accounting for the rostrocaudal axis
reversal seen between the blastula and tadpole stages. The primordia of the notochord
(No), the anterior and posterior somites (AS, PS), the lateral plate mesoderm (LP), the
heart (Ht), and the head mesoderm (H) are indicated. The rostrocaudal (i.e.,
anteroposterior) and dorsoventral aspects of the blastula (which are the same as in the
fertilized egg shown in Fig. 7.9) and of the tadpole are indicated. (After Gerhart, 2002,
and Lane and Sheets, 2002.)

induction above) but also a recognizable notochord and somites will


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