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to the terminal filum at the end of the spinal cord.
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BOX 9.2 EPIGENESIS
Epigenesis is the study of environmental influences acting upon and modifying the individual
genetic program (Wessel 2009). The theory of epigenesis was first proposed in the fourth
century BC by Aristotle in On the Generation of Animals. Aristotle, a truly Philo-physicist
(remember Chapter 1), asked himself if an organism exists from the beginning, or if it devel-
ops in a process similar to the knitting of a fisherman’s net. In this way, Aristotle sparked the
controversy between two possible answers: the preformationist and the epigenetic theories.
Of course, Aristotle privileged the knitting metaphor—the epigenetic theory. However, the
debate prolonged many centuries, and it was insoluble without awareness of the existence of
cells, DNA and genes. Only in the latter half of the twentieth century, more information about
the cell and its constituents were gathered, and it was recognized that embryos develop by
epigenesis. Nowadays, we are aware that embryogenesis provides the most striking example
of epigenetics at work, although we still need to know the details of how a ball of identi-
cal pluripotent cells differentiates into many cell types and organs in response to a network
of physical and chemical environmental signals (Cañestro et al. 2007). After sequencing
the genome of different species, it is evident there are extensive similarities in DNA among
diverse organisms. A natural question arises: Where do the differences come from? The the-
ory of Evo-Devo, which is the nickname for Evolutionary Developmental Biology, proposes
that morphological diversity among species is, for the most part, not due to differences in
functional genes, which encode proteins for cellular maintenance and building, but in genetic
switches that are used to turn genes on and off (Carroll 2005). These switches are sequences
of DNA that do not code for any protein and are part of what was called “junk DNA.” They
are activated by proteins encoded by regulatory genes. Humans share many functional genes
with other creatures, but according to the Evo-Devo theory, the diversity of organisms is due
primarily to evolutionary modifications of switches and the genetic regulatory network. The
master genes constrain the morphology that organisms can assume, and the notion that every
trait can vary indefinitely is not valid according to Evo-Devo.
9.5.2 biology: regeneraTion of Tissues
Regeneration of biological tissues is a phenomenon that is closely related to embryonic develop-
ment. Animals, such as newts and hydra, show remarkable powers of regeneration when parts of
their body are removed. Not many animals can survive decapitation; hydra not only survives but
regenerates a new head. Hydra is a small glove-shaped animal with tentacles for catching prey at
one end and a sticky foot at the other. One can split a hydra into two parts, and within a few days,
two new complete hydrae will form (Figure 9.9). Regeneration requires changing the state of the
cells and remodeling the tissues because it occurs even when all cell multiplication is prevented.
Growth happens only when the animal starts feeding again.
A formal explanation for the regeneration of the hydra entails the possession by cells of posi-
tional information. If the cells know where they are in the animal, they can work appropriately
(Wolpert 2008). The cells know where they are if they are in the head or the foot because the head
produces an inhibitor that diffuses down the body and prevents any of the other tissues from making
a head. When the head is removed, the concentration of the inhibitor falls, and a new head can now
be made. Once the head has regenerated the gradients are reestablished. A similar mechanism, but
of course reversed in space, operates at the food end.
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Cut
Regeneration
FIGURE 9.9 Regeneration of hydra.
9.5.3 biology: PhylloTaxis
In his 1952 paper, Turing proposed that his theory might be useful to explain also phyllotaxis, which
is the regular arrangement of leaves on plant stems. Turing’s idea was that an activator-inhibitor
system of hormones acting at the growing tip of a plant defines the spots that grow into buds on the
cylindrical stem. Leaves and flowers are formed from the shoot apical meristem, 10 triggered by the plant hormone auxin. Recently, it has been shown (Reinhardt et al. 2003) that auxin is transported
through plant tissues by specific carrier proteins. Existing leaf primordia act as sinks, redistributing
auxin and creating its heterogeneous distribution in the meristem. Auxin accumulation occurs only
at certain minimal distances from existing primordia, defining the position of future primordia and
inhibiting the formation of any new buds nearby. This model for phyllotaxis accounts for its reitera-
tive nature, as well as its regularity and stability.
9.5.4 biology: animal markings
Many animals have fascinating color patterns on their skin. There is not a real consensus on what
many of these markings are for. In some species, the markings play as camouflage. The camouflage
can be cryptic or disruptive. It is cryptic when the patterns blend in and match their surroundings, so
the animal can hide from predators. An example is the baby tapir who is born with a reddish-brown
pattern of stripes and spots helping to hide it in the dappled forest light. The camouflage is disrup-
tive when it works by breaking up the outlines of the animal, like in the leopard. In other species,
the color patterns may play other important roles in kinds of behavior such as shoaling, mate choice,
and antagonistic displays.
In the 1980s, Meinhardt (1982) and the mathematical biologist Murray (2003) showed inde-
pendently that Turing’s theory offers a plausible explanation for a wide range of animal pigment
patterns, from mammals like zebras, leopards, to fishes and seashells (Figure 9.10). The basic
idea is that morphogens turn on or off genetic pathways that stimulate the production of pigments.
10 In plants, the meristem is the tissue containing undifferentiated cells (meristematic cells), found in zones of the plant where growth can take place. The shoot apical meristem gives rise to organs like the leaves and flowers, while the root apical meristem contains the meristematic cells for the root growth. The meristematic cells of plants can be compared to animal stem cells, which have an analogous behavior and function. The term meristem derives from the Greek word
μερίζειν (merizein), meaning to divide, in recognition of its inherent function.
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FIGURE 9.10 Examples of pigment patterns in animals.
In mammal skins, the pigment is melanin, and the cells that contain melanin are called melano-
cytes, which are found in the basal, or innermost, layer of the epidermis. There are essentially only
two kinds of melanin: eumelanin (from the Greek ευ- μέλας that means good-black), which results
in black or brown, and pheomelanin (from φάεος that means bright), which results in yellow or
reddish. Both types of melanin are made of cross-linked polymers based on the amino acid
tyrosine; they differ in the overall chemical composition and structure. It is believed that whether
or not melanocytes produce melanin depends on the presence or the absence of chemical activators
and inhibitors. Turing’s RD model has been demonstrated effective in reproducing the broken ring
markings characteristic of leopards and jaguars (Liu et al. 2006) and the patterns of lady beetles
(Liaw et al. 2001).
An essential characteristic of the stationary pattern made by the RD mechanism is its robustness
against perturbations. As far as the patterning process works, the resulting structure can autono-
mously rearrange in a manner that is very specific to the RD mechanism. When an animal with a
stripe pattern grows, the spacing of the stripes becomes wider. Therefore, the growth of the body
tends to change the spacing of the pattern continuously. Since an RD mechanism makes the pattern,
some rearrangement occurs to keep the original spacing. Kondo and Asai (1995) observed in vivo
precisely these changes in tropical angelfish Pomacanthus. If the stripes of the growing fish exhibit
branch points (Figure 9.11), their division occurs by the horizontal movement of the branch points, whereas if there are no branch points, new stripes emerge between the old stripes.
Time
FIGURE 9.11 The growth of the angelfish Pomacanthus is accompanied by horizontal movement of
branch points and division of stripes. (Reprinted from Semin. Cell Dev. Biol. , 20, Kondo, S. and Shirota, H., Theoretical analysis of mechanisms that generate the pigmentation pattern of animals, 82–89, Copyright
2009, with permission from Elsevier.)
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263
Laser
Response
ablation
Time
FIGURE 9.12 Four snapshots of the experiment performed by Yamaguchi et al. (2007) and regarding the
laser ablation of melanophores belonging to two dorsal stripes of zebrafish. (Reprinted from Semin. Cell Dev.
Biol. , 20, Kondo, S. and Shirota, H., Theoretical analysis of mechanisms that generate the pigmentation pat-
tern of animals, 82–89, Copyright 2009, with permission from Elsevier.)
Yamaguchi et al. (2007) ablated by laser the melanophores in two dorsal stripes of zebrafish and
continuously eliminated new melanophores developing in the area (Figure 9.12). This operation
made a broad region lacking melanophores, and induced a dynamic dorsal of the remaining ventral
melanophore stripe to fill the space. The rearrangement began by forming a bell-shaped pattern to
fill the vacant space. This dynamic response of the pattern confirms its intrinsic RD mechanism.
9.5.5 ecology, sociology, and economy
Social animals and plants might use the local self-activation and long-range inhibition Turing-type
mechanism to produce a wide variety of ecological structures. A proven example is the cemetery
formation in Messor Sancta ant colonies (Theraulaz et al. 2002). Messor Sancta ants collect
the bodies of expired colony members and arrange them in piles. The ants constantly pick up and
redistribute the bodies, producing a kind of “diffusion” of corpses. Some piles form, and after a
certain time, several clusters are generated. Over time, some clusters grow and others disappear,
leading finally to a steady state with a stable number of clusters. Because ants are more likely to
drop a body on a pile as the pile gets larger and larger, there is a positive feedback action controlling
their growth. There is also long-range inhibition because the region surrounding a big pile gets free
of bodies and it reduces the probability that a new cluster forms nearby. The example of cemetery
formation in Messor Sancta ant colonies spurs researchers to look for Turing’s morphogenesis in
other collective behavioral patterns, such as network formation, nest construction in termites, and
grouping even in higher organisms.
For example, it has been demonstrated that a Reaction-Diffusion model can explain the phenom-
enon of crime hotspots (Short et al. 2010) in neighborhoods with anomalously high crime rates.
Potential crime targets, such as homes, automobiles, or people, are continuously distributed in the
model, and motivated offenders (activators) search for suitable targets. In the absence of an inhibit-
ing agency, such as a security measure or a police force, the offenders commit their crimes. When
the known positive feedback action, in which crime induces more crime, holds, a Turing structure of
hotspots originates. Such a pattern of hotspots is tough to be eradicated. In fact, focused inhibition
induces merely the Turing pattern of hotspots to move or mutate in shape, but not to disappear.
Turing’s patterns are important also in political economy. When science tries to rationalize
human agglomerations at different spatial scales, like the North-South dualism, the emergence of
cities, or the emergence of commercial districts within cities (Xepapadeas 2010), the theory of
Turing’s patterns is valuable. Moreover, Turing’s model is useful when we deal with the economic
management of ecosystems, like fishery management, spatial pollution or water pricing. In fact, the
theory may suggest the formulation of regulatory policies with spatial features.
9.5.6 geomorPhology
The generation of structure from initially structure-less systems is not restricted to living beings. An
example is the formation of sand dunes. One would expect that the wind distributes the sand evenly
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FIGURE 9.13 Examples of sand ripples.
in the desert. But the opposite occurs. Since sand transport is highly sensitive to wind speed, local
changes in wind velocity alter the pattern of sand deposition. A local minor accumulation of sand
may be triggered by tiny stochastic variations or local surface variation that affects airspeed. Sand
dunes arise from sand deposition behind a minor wind shelter (Figure 9.13). This deposition accelerates the further accumulation of sand. In fact, the growth of the dune increases the wind-shelter
effect and enhances sand deposition even further. In doing so, the dune acts as a sink, removing sand
from the wind and suppressing the formation of other dunes nearby. Similarly, erosion of rocks by
water proceeds faster at some slight depression. In fact, more water collects in the incipient valleys,
causing that the erosion proceeds there more rapidly. Sand or water that accumulates at a particular
location cannot contribute to the process at another position. In fact, next to a river or a lake, there
are no other rivers or lakes (Meinhardt 2009).
9.5.7 The nexT develoPmenT of Turing’s Theory: The mechanochemical PaTTerning
In his seminal paper on the chemical basis of morphogenesis, Turing declared the importance of
mechanics in morphogenesis. Although he was aware of the relevant role of both the chemical and
mechanical part of morphogenesis, he neglected the mechanical contribution for computational
reasons. There were no digital computers available, yet. But, today it is indeed clear that active
mechanical processes, like transport along cytoskeletal filaments (for more information about the
cytoskeleton, read Box 9.3 of this chapter), cytoplasmic flow and endocytosis, play essential roles in
patterning at the cell and tissue levels along with reactions and diffusion events.
The diffusion grounds on the Brownian motion. The Brownian motion is fast over short dis-
tances, but slow over long ones because it is not unidirectional but random. The average distance
traveled by a morphogen having D as its own diffusion coefficient, and after a time interval Δ t is
λ ≈ D( t
∆ ).11 If the morphogenetic species participates in chemical reactions that deplete it with
a rate constant k , its lifetime is τ = ( 1 , and the distance it covers will be λ ≈
τ
D = D / k .
kd )
d
d
In the case of Turing’s mechanism, the two morphogens having D and D as diffusion coefficients,
X
Y
and τ and as lifetimes, originate a pattern that has a characteristic wavelength
X
τY
λ given by
1
1
1
1
1
=
−
≈
−
[9.40]
2
2
2
λ
λ X λ Y
DXτ X
Y
D τ Y
11 Remind exercises 3.10 and 3.11.
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BOX 9.3 CYTOSKELETON
The cytoskeleton is a network of protein fibers that permeate the entire cell. It gives the cell
structure as well as motility. In metaphorical terms, the network of protein fibers plays as the
bone structure of the cell but also as the highway system of the cell. There are three types
of fibers within the cytoskeleton: (I) microfilaments, (II) intermediate filaments, (III) micro-
tubules. (I) The microfilaments are the thinnest of the protein fibers; their diameter ranges
from 6 to 7 nm. They are composed entirely of one type of linear protein called actin. One
important use of microfilaments is in muscle contraction. During muscle contraction, the pro-
tein myosin bound to actin “walks” along the filament creating the contractile motion. Actin
filaments are also involved in the cell movement and division. (II) The intermediate filaments
are rope-like and are composed of different types of proteins; they are thicker than microfila-
ments. In fact, their diameter is about 10 nm. Just like microfilaments, intermediate filaments
give the cell tensile strength and provide structural stability. All the cells have intermedi-
