6.3 Signals and Patterns
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signaling species. The scale of a signaling pattern is fixed by the diffusion lengths
of the morphogens, while in reality development patterns are scaled by the size of
an organism; as an extreme example, a mouse and a giraffe have the same number of vertebrae. A variety of mechanisms have been suggested to rectify this contradiction. Some naive attempts suggested doubling a signal by either a counterpropagating signal or a sink at the opposite edge – an arrangement that becomes
forbiddingly clumsy in the case of two-dimensional patterning and in the presence of
several morphogens. Making decay rates of a morphogen dependent on its concentration levels does not help either; it just deforms the morphogen profile. The scaling
problem could be solved by some kind of global control. For example, having morphogen degradation depend on some chemical species present in a fixed amount
and uniformly distributed in a developing embryo would automatically make the
morphogen gradients scale-invariant, and it could also act in the same way on all
morphogens diffusing in different directions. However, global agents require a fast
mechanism for sustaining their uniform concentration, and this is unlikely to exist
in real tissues.
Naama Barkai and her students have suggested two ways to arrange global control dynamically. One way is to employ a readily diffusible molecule, a kind of
“global agent” that “shuttles” the morphogen around, and another protein that breaks
the shuttle and releases the active morphogen elsewhere (Ben-Zvi et al, 2008). In another model (Ben-Zvi and Barkai, 2010), the role of a global regulator is played by
an “expander” molecule that broadens the morphogen distribution but is repressed
by the morphogen, so that, when the morphogen spreads over the entire domain, the
production of the expander stops and a size-dependent morphogen distribution is
established. Since differentiation of tissues takes place during growth of the tissue,
advection and dilution due to division and migration of cells should be important
factors. Averbukh et al (2014) presented a theoretical model assuming that cells divide when they feel an increase in the morphogen level, and this leads to the right
scaling with size. There are plenty of other papers on this subject, but different
mechanisms coming from the same research group are a good indication that Nature might also sustain proportional development of animals, whatever their size, by
different means. Genetic patterning must not be directed by morphogens in a strictly
hierarchical way, but include dynamic feedback loops.
Besides development processes defining the general body plan and locations of
specific organs, there are less prominent ones, generating repetitive regular patterns,
such us segmentation, separation of fingers, location of hair follicles, bristles or
feather buds, stripes or spots on mammal fur, structuring of insect wings, or the
units of compound insect eyes. It appears at first sight that Turing’s symmetrybreaking scheme should work straightforwardly here – but Nature rarely concedes
to make things simple. Although patterns of fur coloration can be simulated in apparently convincing detail with the help of the universal pattern-forming model, the
FN equation (Sect. 3.5), this has nothing to do with their actual mechanism of formation. Segments do not form by symmetry breaking but grow consecutively in
the wake of a signaling wave propagating towards the anterior (Pourquie, 2003).
Other processes, though based on the same kind of activation combined with lateral
93
signaling species. The scale of a signaling pattern is fixed by the diffusion lengths
of the morphogens, while in reality development patterns are scaled by the size of
an organism; as an extreme example, a mouse and a giraffe have the same number of vertebrae. A variety of mechanisms have been suggested to rectify this contradiction. Some naive attempts suggested doubling a signal by either a counterpropagating signal or a sink at the opposite edge – an arrangement that becomes
forbiddingly clumsy in the case of two-dimensional patterning and in the presence of
several morphogens. Making decay rates of a morphogen dependent on its concentration levels does not help either; it just deforms the morphogen profile. The scaling
problem could be solved by some kind of global control. For example, having morphogen degradation depend on some chemical species present in a fixed amount
and uniformly distributed in a developing embryo would automatically make the
morphogen gradients scale-invariant, and it could also act in the same way on all
morphogens diffusing in different directions. However, global agents require a fast
mechanism for sustaining their uniform concentration, and this is unlikely to exist
in real tissues.
Naama Barkai and her students have suggested two ways to arrange global control dynamically. One way is to employ a readily diffusible molecule, a kind of
“global agent” that “shuttles” the morphogen around, and another protein that breaks
the shuttle and releases the active morphogen elsewhere (Ben-Zvi et al, 2008). In another model (Ben-Zvi and Barkai, 2010), the role of a global regulator is played by
an “expander” molecule that broadens the morphogen distribution but is repressed
by the morphogen, so that, when the morphogen spreads over the entire domain, the
production of the expander stops and a size-dependent morphogen distribution is
established. Since differentiation of tissues takes place during growth of the tissue,
advection and dilution due to division and migration of cells should be important
factors. Averbukh et al (2014) presented a theoretical model assuming that cells divide when they feel an increase in the morphogen level, and this leads to the right
scaling with size. There are plenty of other papers on this subject, but different
mechanisms coming from the same research group are a good indication that Nature might also sustain proportional development of animals, whatever their size, by
different means. Genetic patterning must not be directed by morphogens in a strictly
hierarchical way, but include dynamic feedback loops.
Besides development processes defining the general body plan and locations of
specific organs, there are less prominent ones, generating repetitive regular patterns,
such us segmentation, separation of fingers, location of hair follicles, bristles or
feather buds, stripes or spots on mammal fur, structuring of insect wings, or the
units of compound insect eyes. It appears at first sight that Turing’s symmetrybreaking scheme should work straightforwardly here – but Nature rarely concedes
to make things simple. Although patterns of fur coloration can be simulated in apparently convincing detail with the help of the universal pattern-forming model, the
FN equation (Sect. 3.5), this has nothing to do with their actual mechanism of formation. Segments do not form by symmetry breaking but grow consecutively in
the wake of a signaling wave propagating towards the anterior (Pourquie, 2003).
Other processes, though based on the same kind of activation combined with lateral