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genomic program for embryonic development. In some
animals the regeneration of whole body parts can occur in
the adult, but evidence indicates that the underlying
processes are different from the spatial control processes of
embryogenesis.
Specification in the earliest stages of embryogenesis
depends at least in part on initial anisotropies, as above.
Later spatial specification in embryos, and in body part
subdivision, is usually accomplished through sequences of
inductive signaling where there is generally only one
response to the signal, and where signaling is often, and in
some systems always, short range. One such system is the
pregastrular sea urchin embryo, to which pertain the
examples of GRN-mediated spatial specification
processes discussed in the following section. Here we
consider the dynamics of spatial specification in this
embryo. Already by gastrulation (~ 600 cells), this embryo
has constructed a mosaic of at least 10 distinct territorial
spatial regulatory states, each giving rise to a different part
of the completed post-gastrular larva.
What determines the tempo at which spatial regulatory
state changes occur in this embryo? Detailed kinetic
expression measurements for gene cascades in this system
describe the dynamics of progression from one regulatory
step to the next ('step time'). Although it had been noticed
earlier in experimental GRN analyses [14,15] , a consis-
tently amazing result was the great regularity of the step
time throughout many hours and many steps [45] . Gene to
gene, the whole system runs on a similarly paced regulatory
clock.
What determines the beat of the clock and why it
operates the way it does is a particularly interesting
problem, because despite the complexity of the process of
embryonic development, it is temperature adjusted. Thus
different species of sea urchin that live at different
temperatures develop at different rates, but these devel-
opmental rates (e.g., time from fertilization to gastrulation)
are predictable from one another because they closely
follow the same Q10 rule that applies to basic molecular
biology processes such as RNA or protein synthesis. That
is,fromcoldwateranimalstofliestomammals,foreach
10 C temperature change the real-time rate for these
molecular processes changes by a factor of about 2 [5] .
This turns out to provide a valuable clue to the clock-like
behavior of at least some developmental systems. In 2003,
a dynamic a priori analysis of step time in sea urchin
embryos was carried out by Bolouri and Davidson [43] ,in
which a model of cis-regulatory occupancy by transcrip-
tion factors was constructed, based on thermodynamic
principles [44] ,andcis-regulatory occupancy was related
mathematically to the rate of transcriptional initiation and
then combined with synthesis and turnover kinetics. This
was essentially a first-principles estimation of what the
step time should be for sea urchin embryos, assuming
typical values of relative transcription factor
DEVELOPMENTAL GRN DYNAMICS
GRN dynamics denotes the changes in regulatory state
encoded by GRN circuitry with time. Thus far the vast
majority of dynamic regulatory processes that have been
analyzed in developing animal systems are sequential
changes in regulatory state that take place in the same cells.
Over time, regulatory states change in these given cells, for
example as a result of receiving signals, or in processes of
stem cell differentiation, such as lineage choice functions in
which given pluripotential cells respond to external
conditions by activating one or another regulatory state.
Such biological processes have been the subject of
numerous ODE kinetic models (e.g.,
37] .
However, dynamic models of sequentially occurring
changes in state within given cells or domains do not
address the mechanisms causing changes in spatial regu-
latory state, with which we have so far been concerned.
Dynamic modeling of GRN outputs has been used to
analyze several developmental mechanisms that execute
spatial specification. The main function of the GRNs that
controlbodyplanformationistosetupprogressively
subdivided discrete regulatory state domains in space.
They do this dynamically, of course, but the architecture
of the GRNs that specify this process cannot be derived
from the kinetic output of the network; rather, the kinetics
can be derived from the GRN architecture if sufficient
kinetic parameters are known. An example in which GRN
architecture was used to construct a kinetic model
concerns the dynamics with which spatial patterns of gap
gene expression in the 14th cleavage cycle Drosophila
embryo are generated [38,39] . Here previous studies had
revealed much of the GRN topology, and this topology
wasusedintheformulationofanODEmodel.Alarge
number of synthesis, decay and other kinetic parameters
were extracted from a quantitative high-resolution
imaging dataset and the observed process can be recon-
structed when the model is run, with a few additional
interactions indicated. In this system the constrained
diffusion of transcription factors among nearby syncytial
nuclei provides the spatial inputs to the genetically hard-
wired transcriptional response system indicated by the
GRN architecture. A second example is afforded by
analyses of response to graded Hedgehog signaling in both
the amniote neural tube [40,41] , and in the Drosophila
wing disc [42] . But in a large number of developmental
contexts graded signal
[26
31,34
e
e
DNA equi-
librium constants, and using canonical transcription,
protein synthesis, and turnover rates that had been
measured for these embryos at 15 C. There were two
results that proved to be of immediate explanatory value
e
response
is not
an issue.
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