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wg WG

ptc PTC

cid CN



Fig. 10.6 Interactions among products of the ¬ve genes of the Drosophila
segment-polarity network in the model of von Dassow et al. (2000): WG, Wingless; EN,
Engrailed; HH, Hedgehog; CID, Cubitus interruptus (whole protein); CN, repressor
fragment of Cubitus interruptus; PTC, Patched; PH, Patched“Hedgehog complex. The
interactions indicated by broken lines were added after simulations showed the
insuf¬ciency of the solid-line interaction alone in reproducing the normal
segment-polarity spatiotemporal pattern of gene expression (see Fig. 10.7). The ellipses
represent mRNAs, the rectangles proteins, the hexagon a protein complex; the arrows
indicate positive interactions; the lines terminating in circles, negative interactions.
Cubitus interruptus is constitutively expressed at a basal level, represented by the plus sign
in the rhombus. (After von Dassow et al., 2000.)

modules without changing their intrinsic behaviors” (von Dassow
et al., 2000). These investigators therefore formulated a dynami-
cal model based on the unidirectional gene regulatory interactions
known to accompany the establishment of segment polarity in
Drosophila, where it has been best studied (see, e.g., Bejsovec and Wi-
eschaus, 1993). The key components they considered were the tran-
scription factors Engrailed and Cubitus interruptus, the secreted mor-
phogens Wingless and Hedgehog, the Hedgehog receptor Patched, and
CN, a proteolytic fragment of cubitus interruptus generated during
normal development that negatively regulates Wingless and Patched
at the transcriptional level (Fig. 10.6).
The main goal of this study was to discover parameter sets that
would reproduce in a robust fashion the experimentally determined
spatial expression of the major genes during the establishment of seg-
ment polarity (Fig. 10.7A, B). Like other dynamical systems (see Chap-
ter 3), different versions of the segment-polarity module can be rep-
resented as individual points in a multidimensional space in which
the coordinates are the system parameters. In the random search that
von Dassow and coworkers performed on the parameter space of the


ptc ptc


Fig. 10.7 Gene expression patterns of the segment-polarity genes in the Drosophila
embryo and simulations in the model of von Dassow and coworkers. (A) The spatial
expression pattern of wingless (wg) and engrailed (en) superimposed on an outline of the
embryo. The parasegmental boundaries divide columns of wg-expressing cells (green)
from columns of en-expressing cells (blue). (B) A schematic representation of the
experimentally observed embryonic pattern of expression of the genes used in the
model (abbreviations as in Fig. 10.6). For simplicity a single strip of twelve cells,
corresponding to the boxed region in A, is shown. In each row, only cells expressing the
indicated gene are shown in color; the others are shown in black. The full
segment-polarity gene expression pattern is obtained by superimposition of the eight
rows. (C) The best simulation pattern that was achieved with the interactions indicated
by the solid lines in Fig. 10.6. (D) The pattern achieved by addition of the interactions
indicated by the broken lines in Fig. 10.6. The simulated patterns achieved with this set of
interactions were, in general, truer to the embryonic system (A), though in this
particular simulation the expression of patched was suppressed. The experimental and
model patterns are distinguished by the use of different symbols (ovals and hexagons
respectively). (After von Dassow et al., 2000.)

segment-polarity module it was not feasible to include all the nu-
merous gene interactions that characterize this module. The initial
decision to choose a hierarchy of unidirectional interactions was mo-
tivated by the existence of such a hierarchy for the generation of
the pair-rule expression patterns (see above) directly preceding the
operation of the segment-polarity module.
Signi¬cantly, when von Dassow and coworkers used only the hier-
archical interactions represented by the solid lines in Fig. 10.6, despite
extensive calculations they found no suitable parameter sets to arrive
at the target patterns of gene products (i.e., the true patterns of key
gene products generated by the Drosophila segment-polarity module).
The majority of randomly chosen parameter sets caused either the
model components to oscillate strongly or some components to be
expressed ubiquitously while others were repressed everywhere. The

closest they could come to the target pattern (i.e., obtaining it once
in about 3000 randomly chosen parameter sets) is the pattern shown
in Fig. 10.7C. No parameter sets produced stable asymmetric patterns.
When, however, the investigators added two additional interactions, a
positive feedback loop by which wg activates its own production and
a negative feedback loop by which CN inhibits the expression of en,
they were able to achieve remarkable success in ¬nding parameter
sets that reproduced the experimental patterns. An example of one
such pattern is shown in Fig. 10.7D.
Equally remarkable was the tolerance to parameter variation ex-
hibited by this modi¬ed model. Because the actual values of the gene
product synthesis and the decay rates and other parameters were
not known, simulations were performed over the range of biologi-
cally plausible values, i.e., several orders of magnitude. Nonetheless,
for any of the 48 model parameters a random choice of its value
was compatible with the desired behavior roughly 90 percent of the
time. For some parameters, reasonable matching to the target pattern
occurred despite variation of 100--1000 in their values (von Dassow
et al., 2000). The authors concluded that the network™s ability to pro-
duce a realistic segment-polarity pattern is intrinsic to its topology
(i.e., the links and feedback relationships in the pattern of gene--gene
interactions) rather than to speci¬c quantitative tuning.
Despite containing many hierarchical interactions, the core
pattern-forming mechanism embodied in the gene network proposed
by von Dassow and coworkers (Fig. 10.6) is ˜˜emergent” in the termi-
nology of Salazar-Ciudad et al. (2000, 2001a, b). This distinguishes it
from the largely hierarchical gene network that produces the ear-
lier forming pair-rule pattern in Drosophila (Figs. 10.2 and 10.3). The
feedback loops present in such emergent networks (for example, the
broken lines in Fig. 10.6) predispose these networks to exhibit bistable
behavior (Ingolia, 2004), i.e., small displacements of a system in its
state space can cause it to switch abruptly between alternative stable
nodes or orbits (see Chapter 3). Thus the cells in the model of von
Dassow et al. (2000) can each produce either Engrailed or Wingless but
not both at the same time in a way that is consistent with the true
expression pattern. Ingolia (2004) has suggested that it is dynamical
bistability (as a consequence of the network topology), rather than
any other speci¬c aspect of the von Dassow model, that is responsi-
ble for its robustness and that a large proportion of realistic models
that contain this feature will be similarly resistant to perturbations.
Assuming this class of emergent models is a valid representa-
tion of the segment-polarity module, evolution has a wide latitude
in altering key parameter values by genetic mutation, so long as the
bistable dynamics is preserved. For any parameter choices within the
acceptable range, the module will be buffered against developmental
˜˜noise,” i.e., random biochemical ¬‚uctuations that inevitably occur
during the course of embryogenesis and other biological processes
(Barkai and Leibler, 2000; Vilar et al., 2002).
As described above, in certain cases evolution may have trans-
formed an originally self-organizing developmental mechanism into

a hierarchical system of gene interactions like the one that generates
the Drosophila pair-rule pattern or speci¬es the mesoderm and endo-
derm during gastrulation in the sea urchin embryo (Oliveri and David-
son, 2004). In exchange for the molecular precision afforded by such
hierarchical mechanisms, systems evolved in this fashion must neces-
sarily relinquish the kind of robustness inherent to emergent mecha-
nisms. In such cases other mechanisms of robustness may evolve, such
as gene duplication (Wilkins, 1997) and other mechanisms of func-
tional redundancy (Tautz, 1992; Cooke et al., 1997), in which distinct
processes act in parallel to serve the same developmental ends. Since
complex forms (e.g., the original segmented arthropod, see above)
plausibly originated by dynamical mechanisms acting in concert with
genetic mechanisms (Newman and M¨ ller, 2000; Salazar-Ciudad et al.,
2001a, b), the replacement of emergent by hierarchical mechanisms
would also have had the result that organisms became less ˜˜evolv-
able” (Riedl, 1977; Wagner and Altenberg, 1996; West-Eberhard, 2003).
As the example of the segment-polarity module shows, however, by
retaining aspects of their physical character, living systems can re-
main self-organizing and responsive to the external world. This sets
limits on the tendency of living processes to become fully assimilated
into genetic hierarchies and, in turn, justi¬es formulating a biological
physics of even modern-day, highly evolved organisms.

Organismal forms have not always been generated by the highly
integrated genetic programs characteristic of modern multicellular
species. The ancient progenitors of modern metazoan animals were
clusters of nucleated cells that, despite being in aggregates, retained
their ability to locomote and change their relative positions. Once
these emerged more than 700 Ma ago, physical processes irrelevant
or marginal to single-cell life came into play. These included liquid-
like tissue behavior, the capacity to sustain diffusion over distances
on the scale of the whole organism, reaction--diffusion coupling, dif-
ferential adhesion, and the cyclical regulation of intercellular adhe-
sion. These mechanisms, in turn, made developmental gradients, tis-
sue multilayering, lumen formation, and segmentation inevitable,
thus providing the basic ingredients of modern-day developmental
systems. The morphological templates that arose by means of basic
physical mechanisms in the early period of metazoan evolution were
consolidated and reinforced by later genetic change, with hierarchi-
cally organized genetic mechanisms often coming to substitute for
conditional physical mechanisms. This may have led to some devel-
opmental modules, such as the early stages in Drosophila segmenta-
tion, taking on the character of ˜˜hard-wired” genetic programs. No
contemporary embryonic system, however, has evolved away from de-
pendence on the physical, and therefore conditional and dynamical,
properties of living cells and tissues for generation of its patterns and

Absolute temperature The temperature measured in kelvins, K
(0 K ≈ ’273 —¦ C).
Acrosome A large vesicle in the sperm head that releases its contents by
rapid exocytosis upon encountering the vitelline membrane. The
acrosomal contents, a set of enzymes, locally digest the vitelline
membrane enabling the sperm to reach the egg cell membrane.
Actin A globular protein (G-actin) that can associate into polymers (F-actin)
to form cytoskeletal micro¬laments involved in contractile and motile
functions of cells.
Activation energy The minimum amount of energy needed to bring
potentially reacting chemicals to a state in which they can react.
Activator A molecular component in a biochemical reaction network or
circuit that enhances the production of itself or another component.
Active transport The movement of a molecular component across a cell
membrane by a process that requires expenditure of free energy.
Adherens junction A macromolecular adhesion complex between apposing
sites on two adjacent cells, consisting of cadherins and accessory proteins
linking the complex to the actin cytoskeleton.
Allantois A sac that develops from the posterior portion of the developing
digestive tube in reptiles, birds, and mammals; in mammals it
participates in the formation of the umbilical cord.
Amino acid A class of organic molecules in which a carbon atom
(alpha-carbon) is attached to a hydrogen atom, an amino group (-NH3 ),
a carboxy group (-COOH), and a side chain. The genetic code speci¬es
20 amino acids with distinct side chains, which are used in the synthesis
of proteins.
Amino terminus (N-terminus) One of two ends of a protein: the end
containing a free (uncombined) amino group.
Amoeboid locomotion A type of cell movement that depends on changes
in state and ¬‚ow of cytoplasm.
Amphibian A type of vertebrate organism (e.g., frogs, toads, salamanders)
adapted to life in aquatic and terrestrial environments at different stages
of their life-histories.
Amphipathic A molecule (e.g., a membrane phospholipid) that contains
both hydrophilic and hydrophobic regions.
Anaphase A stage of cell division in eukaryotic cells, immediately after the
chromosomes are aligned at the metaphase plate, during which the two
sister chromatids of each replicated chromosome are pulled apart by the
mitotic apparatus toward the opposite poles of the spindle.
Angioblast A mesenchymal cell that gives rise to blood vessels.
Animal pole The point on the surface of a telolecithal egg (i.e., one with
nonuniform distribution of yolk) or early embryo at the center of the


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