In the book

1
In the book Models of Biological Pattern
formation (Academic Press, 1982) I described in
chapter 14 models for segmentation and somite
formation.
In the following, an outline of these models is
provided. To see the animated simulation press F5
A TEX-remake of the book is available on our
website http//www.eb.tuebingen.mpg.de/meinhardt/
82-book Hans Meinhardt Max-Planck-Institut für
Entwicklungsbiologie Tübingen / Germany
2
Digits, segments, somites
A type of structure which is frequently
encountered in higher organisms consists of a
sequence of similar but not identical
substructures. Segments in insects, the somites
and the digits of vertebrates are examples.
Usually their total number is precisely regulated
As the basic mechanism we proposed that cell
states are involved that locally exclude each
other but activate each other on long
range Meinhardt and Gierer (1980) J. theor.
Biol., 85, 429-450
3
Digits, segments, somites
This mechanism found strong support by the later
discovered logic in the engrailed-wingless
interaction engrailed and wingless are locally
exclusive engrailed activates wingless in the
adjacent cell via hedgehog. In turn, wingless
molecules, transported in vesicles, are
absolutely required for the engrailed activation
in the neighboring cell. As predicted, wingless
and engrailed activation is autocatalytic. In
engrailed, the self-enhancement is direct, that
of wingless involves sloppy paired.
4
Digits, segments, somites
To illustrate the properties of such a type of
interaction I used the following set of equations
a and p describe the local autocatalytic feedback
loops, sa and sp the mutual long-ranging help. In
this example it is assumed that the mutual
repression occurs by a common repressor r which
is produced by both autocatalytic loops and that
acts on both. This mutual local exclusion has the
consequence that in one cell only one of the
feedback loop can be active. Booth loops require
the help from the other cell state a and p
expressing cells will appear next to each other.
The mutual repression can also be direct (see
below)
This is Eq. 12.1 from the 82-book only g1 and g2
is substituted by a and p as a label for the
compartmental specifications
5
Digits, segments, somites
To illustrate the properties of such a type of
interaction I used the following set of equations
In this simulation the homogeneous distribution
of a and p becomes instable, high a and high p
expression occur in adjacent cells. This
mechanism show a good size-regulation after
partial removal of one cell type.
6
Digits, segments, somites
If the autocatalytic components are not
diffusible, the border between the two regions
will be absolutely sharp. This is the case in the
engrailed-wingless interaction for the
compartment formation in Drosophila the clonal
borders are sharp and cannot be moved, as
observed. However, if only one cell type remain,
a partial reprogramming may be possible (as
observed after fragmentation of of imaginal
discs)
7
Digits, segments, somites
An important feature of such a system is that it
can generate stripes. Since the different cell
types need each other for mutual stabilization, a
long common border leads to a most stable
situation. The ability to form stripes is
required for many such systems. (In this
simulation above pattern formation is initiated
by a slightly higher level of p (red) in the
right half of the field).
8
Digits, segments, somites
In this alternative example, the interaction
between the two feedback loops occurs not by a
long-ranging mutual activation but by a
self-inhibition (a2/sa). In competing systems, a
help for the other feedback loop or a
self-inhibition is equivalent. The mutual
exclusion is direct (a2 p 2 ). The term
in the first equation can lead to a
threshold decisive for a transition for between
an oscillating and an excitable system (see
below).
(see Eq. 12.2 in the 82-book)
9
Segmentation mutual long range activation of
locally exclusive cell states
In short germ insects segments are sequentially
added at a posterior elongation zone. In a most
simple model using the mechanism described above,
a periodic pattern is generated during posterior
outgrowth. Assumed is a doubling in the
right-most cell. Whenever a particular activation
(compartmental specification) exceeds a certain
extension, a flip to the other activation will
occur. Note that the most-posterior cell
oscillates between the two cell states
10
Segmentation mutual long range activation of
locally exclusive cell states
The simulation above shows the pattern at
successive stages. Note that at a particular
moment, a posterior terminal activation of either
the one or the other type is expected.
This fits with the observation of Damen, Weller
and Tautz (2000), PNAS 97,4515-4519 in the spider
11
Prediction at least three cell states are
required to generate a periodic structure with an
intrinsic polarity
A periodic pattern consisting of an alternation
of two cell states has no intrinsic polarity
A
P
A
P
A
P
An alternation of three cell states has an
intrinsic polarity For Drosophila it has been
shown that the A and the P cells resembling the
incipient anterior and posterior compartment are
indeed separated by two other cells the are
neither A or P. (The separation of one somite
from the next is not yet clear and could be
different in different systems)
Parasegment
A
P
S
A
P
S
A
P
S
Segment
12
Oscillations and spatial pattern formation during
posterior outgrowth
Assumption in the P-state (red) the next HOX
gene is activated, but the transition is
blocked. After transition to the A-state,
activation of the next HOX gene is no longer
blocked, but no activation of the next Hox-gene
one full cycle for a next gene
Top periodic patterns that leads to
segmentation the periodic pattern has
polarity. Below Specifying genes (HOX) genes
The segments formed during outgrowth resemble not
only a periodic structure they carry a
specificity. In the 82-book it was proposed that
the terminal oscillation is also used to activate
the corresponding genes for specification (now
known to be the HOX-genes). According to the
model, if the cells are in one cell state, an
activation of the next (HOX) gene is prepared but
the full activation occurs only after switch to
the other state. Thus, for instance, with each
P-to-A transition, one and only one new
specifying gene was assumed to become activated.
The model describes correctly that both the
sequential and the periodic pattern are precisely
in register with single cell precision (as
observed). Now we know that more than one cycle
has to pass until the activation of the next HOX
gene occurs.
13
As segments in short germ insects, somites in the
ancestral Amphioxus are also formed at a
posterior elongation zone. However.
Remarkable somites on the left and on the right
side appear out of phase in an alternative
sequence (see Schubert, Holland, Stokes and
Holland (2001) Dev. Biol. 240,262-273
14
. in contrast, somite formation in vertebrates
occurs at a substantial distance from the
posterior pole
Wolpert Principles..
At the time I proposed my somite model, almost
nothing was known about the molecular basis of
somite formation. An important piece of
information came from heat shock experiments in
Amphibians. A short heat pulse lead after a
certain delay to some characteristic
perturbations in the somite patterning
15
Such a perturbations lead frequently to a
Y-shaped split of a somite into two or to an
incomplete border between two somites.
Elsdale and Pearson (1979). Somitogenesis in
amphibia. II. Origins in early embryogenesis of
two factors involved in somite specification. J.
Embryol. exp Morphol. 53, 234-267
Such an irregularity is frequently followed by a
second irregularity that compensates partially
the first, allowing that somite formation can
proceed normally. This I regard as a clear
indication that a spatial component is involved
in the patterning.
16
Combining oscillations and spatial pattterning
To see how the oscillation derived for insect
segmentation and patterning in space can be
combined, it is essential to see that the
mechanism shown above can act also as an
oscillator. For instance, if only A cells are
present, the P-cell state will get strong
support, while the support of the A state by the
P cells is missing. Thus, cells will switch from
A to P and for the same reason back to A, i.e,
they will oscillate between the two states. This
works in the same way if self-inhibition is
involved.
Now imagine that only one A cell exists
initially at the anterior end. The direct
P-neighors will be be stabilized, while the other
will continue to oscillate. With each complete
cycle there would be one new pair of A/P
specifications (half-somites).
17
Conversion of an oscillating pattern into a
periodic pattern that is stable in time
In this way the oscillation gives rise to a
regular pattern in space. The non-trivial
prediction was made that a boundary between a
stable and an oscillating pattern sweeps from
anterior to posterior over the field. This
raises, however, the question what makes the
first border?
Time
Position
18
Combining oscillations and spatial pattterning
The assumption was that at the posterior terminal
position a gradient is generated and that a
certain concentration is required to keep the
oscillation going. Cells below a threshold are
unable to oscillate. Now it is clear that this
prediction was correct, the gradient shown in the
simulation in yellow has been identified as FGF.
Palmeirim et al. (1997). Cell 91, 639-648
A comparison with the observation of Palmeirim et
al., 1997 shows the striking correspondence
between the 82-model and the 1997 observation.
19
Combining oscillations and spatial pattterning
A switch between an oscillating or an excitable
system can be accomplished by a baseline
inhibitor level or a Michaelis-Menten type
constant. If is large enough, the a
activation can no longer trigger spontaneously
since the denominator remains finite. The
positional information p (yellow) lowers the
influence of . Thus, if p is high enough (in
the posterior), the system oscillates, otherwise
it is arrested in the p state.
20
(Hox) gene activation under the influence of the
oscillation
The aim was to also explain the sequential
activation of specifying genes. The model
proposed offered a very convenient mechanism. The
number of the oscillations a cell has been made
corresponds unambiguously to its position. Each
more posteriorly located pair of half-somites
proceeds exactly through one more oscillation
cycles. As shown above for insects, this can be
used to activate specifying (HOX) genes (lowest
panel)
Although the precise mechanism of the coupling
between the oscillation and Hox gene activation
is still unclear, there is some evidence for
it Dubrulle, et al., (2001). Fgf signaling
controls somite boundary position and regulates
segmentation clock control of spatiotemporal hox
gene activation. Cell 106,219-232 Zakany et al.,
(2001). Localized and transient transcription of
hox genes suggests a link between patterning
and the segmentation clock. Cell 106,207-217
21
The clock and wave front model of Cooke and
Zemann (1976)
Although Cooke and Zemann did not formulate their
model in a mathematical way, such a model can be
easily provided by the elements of or models. In
the simulation above the wave is generated by an
activator-inhibitor system with a non-diffusible
inhibitor that has a longer half-life then the
activator. A similar assumption was made for the
overall oscillation that takes place in the whole
field (blue). The wave triggers the activation of
a gene for somite formation (brown) in a
switch-like manner. A burst of the oscillation
blocks this activation, leading to a gap in the
gene activation thought to give rise to the
somites. It is easy to see that this model does
not fit the observations, e.g., there are no
waves from the posterior that come to rest in the
somite-forming zone, half-somites do not play a
role, the localization of oscillation does not
play a role, the oscillation is involved in the
separation, not in their determination.
22
Summary

• The model was the first fully mathematically
  formulated model for somite formation. It
  correctly predicted that
• An out-of-phase oscillations occur in the
  posterior PSM
• Activations spreads from posterior towards
  anterior come to rest at the somite forming zone
• Each full cycle adds one pair of A- and
  P-half-somites
• The oscillation that leads to the periodic
  pattern can be used to accomplish a very precise
  activation of (Hox)-genes that specify the
  character of the periodic elements. This issue is
  not yet solved.
• Not yet clear how are somites separated from
  each other

23
A final remark

• The model was proposed in 1982 when nothing was
  known about the molecular basis. Moreover,
  computers were awfully slow at this time. Thus,
  it was necessary to keep the model as simple as
  possible. Therefore, in the model a single
  reaction chain was used to describe
• The Oscillation
• The transition into stable a pattern
• Memorizing A and P specifications
• ? This is certainly too simple but shows the
  essence

24
As mentioned, a TEX-remake of the book is
available on our websitehttp//www.eb.tuebingen
.mpg.de/meinhardt/82-book
Essentially the same model was published in a
proceeding volume Somites in Developmental
Biology (R.Bellairs, D.A.Edie, J.W. Lash, Edts),
Nato ASI Series A, Vol 118, pp 179-189, Plenum
Press, New York as Meinhardt, H. (1986b) Models
of segmentation. (on our website)