3.6 A primer in morphogenesis
and developmental biology
What are the big
questions in
developmental biology?
Phylotaxis – leafs on plants are usually
arranged in specific geometries
(according to the golden mean).
Limb development – what determines
when and how limbs are formed?
Scaling – How come that animals
always have the same proportions no
matter their size?
Growth – How does an organism know
when to stop growing (by the way note
the scaling in the picture below even
though it doesn‘t work physically)?
Morphogenesis - How do you get from a
spherical egg to say a frog?
"It is not birth, marriage or
death, but gastrulation, which
is truly the most important time
in your life."
Lewis Wolpert
3.6.1 Morphogen gradients
First developmental experiments: Willhelm
Roux on sea urchins
Driesch repeats the experiments
and gets very different results
Spemann Mangold experiment –
bringing both sides back together
And now for some physics: Enter
Alan Turing
Turing, Phil. Trans. Roy. Soc. B 237, 37 (1952)
The activator-inhibitor system
shows an instability to fluctuations.
An application to this may be in
Phylotaxis or why do plants know the
Fibonacci series.
In 1969 the world changed...
Lewis Wolpert takes up
Turing‘s ideas
experimentally and
produces his own
mathematical treatment.
Take a source at one end of the embryo
and let the morphogen diffuse through it.
Morphogen diffusion with breakdown
stationary state
with the solution
Wolpert, Journal of theoretical biology 25, 1 (1969)
Once such a gradient exists, it can be
used to encode positional information by
increasing the expression of certain
proteins.
But there‘s more: positional information is
kept when different genes are expressed
– and development is robust (sea urchins
always look the same no matter what you
take away from them... So there‘s
scaling.
How morphogens actually work we‘ll see in example 2...
Chick limb development: the morphogen
sonic hedgehog in the early limb
determines the later fate.
A change in morphogens can also
change the orientation of a limb
Extremity development is crucially
dependent on the right positional
information at a very early stage.
More reaction-diffusion systems and
more physics: Hans Meinhardt
Gierer & Meinhardt, Kybernetik 12, 30 (1972).
Such activator-inhibitor systems can
explain classical polarity experiments.
In sea
urchins
Hörstadius & Wolsky, Roux‘ Archives 135 69 (1936).
In Hydra
Müller, Differentiation 42 131 (1990).
Such reaction diffusion systems of three
different morphogens can also lead to
spatial stabilization.
This isn‘t just an academic plaything –
the proteins MinC, MinD and MinE,
which are important in the division of
E. coli show exactly these oscillations.
Thus leading to an accurate splitting.
Raskin & de Boer, PNAS 96 4971 (1999).
3.6.2 A primer in pattern formation
Start with the Gierer-Meinhardt
equations as an example:
For simplicity, we set ka = sh = 0
dimensionless variables:
gives simpler equations:
Solve them for the homogeneous
steady state (i.e. D = 0 and t = 0):
Then perturb this state with a
harmonic function and only keep terms
linear in da0 and dh0:
This gives the linear system of
equations:
with
There is only a solution with non-zero
da and dh if the discriminant of the
Matrix is zero:
with
The fluctuations only grow if the real
part of w > 0. The critical value is thus
given by Re(w) = 0. If w has complex
values (i.e. b > (a/2)2), the real part is
given by a/2 and hence the condition
is a = 0. Thus
On the other hand, if w is real valued,
then it is only zero if b = 0. This yields:
A spatial pattern can therefore only
develop in an embryo, if ist size
exceeds Lc. As long as the length is
close to Lc, this also implies a polarity,
since the cosine does not recover on
this length scale.
We can do this more generally by
assuming that k is continuous. Then
we look at which wave number
disturbance grows fastest:
while Re(w) > 0
Again we start with the case that w is
complex: then Re(w) = -a/2 and the
fastest growing wavenumber is k = 0.
The fact that w is complex and that
Re(w) > 0 lead to conditions for m
where we are in this case of a growing
homogeneous state that oscillates.
If w is real, we obtain:
and w is is positive if:
All of this is summarized in the
Stability diagram:
growing,
inhomogeneous
pattern
Homogeneous,
static pattern
Oscillating,
homogeneous
pattern
Another set of differential equations
describes a threshold switch
Simulation of animal coatings using
reaction diffusion and a switch
Simulation results for pigmentation
giraffe
lepard
cheeta
3.6.3 An example: The anterioposterior axis in Drosophila.
Nüsslein-Vollhard & Wieschaus, Nature 287 795 (1980).
Three different sets of genes
Nüsslein-Vollhard & Wieschaus, Nature 287 795 (1980).
So there‘s a hierarchy of genes and
proteins in the early development
Reminder – where are we in the
developmental stages...
Lets have a closer look at the gapgenes – their positions determine the
stripes of the pair-rule genes
Interactions (as transcription factors) of
the different gap genes
This can be visualised using
fluorescence probes in vivo....
For instance stripe 2 is given by the
competition of Hunchback, Giant and
Krüppel
All in all there will be seven stripes of
eve expression controlled by different
combinations of the gap-genes
Meinhardt has modelled this much more
elegantly than nature with less
complicated feedback cycles – but
nature sometimes isn‘t elegant...
Meinhardt, J. Cell Sci. Suppl. 4 357 (1986).
But how do proteins act as transcription
factors on a molecular level such that
they can be viewed as morphogens?
See section 3.5 on transcription
Some enhancer sequences for
transcription
Others form fingers which stick out
specific DNA binding sites using Zinc
groups.
Krüppel for instance uses such a transcription factor.
How does one know all this?
Electrophoresis of digested RNA
Then check what it does in vivo.
Or specifically Bicoid binding sites
Map of the hb gene indicating the locations of bcd-binding sites. The
2.9 kb hb transcript is expressed in an anterior domain which
extends from 55-100% egg length, whereas the 3.2 kb transcript
(which is expressed maternally and zygotically) is localized to 025% egg length. A, B and C are the fragments identified in the
experiment shown in Fig. 2. b, Nucleotide sequences of the regions
where bcd protein binds to hb regulatory regions. Base pairs
protected against DNaseI digestion as referred from Fig. 4 are
indicated by a bar below the sequence.
Driever & Nüsslein-Vollhard, Nature 337 138 (1989).
Lets get back to the development of the
anerioposterior axis
The first step is the most important – get
a gradient going à la Wolpert!
Driever & Nüsslein-Vollhard, Cell 54 95 (1988).
Bicoid is known to act as an activator for
hunchback expression.
Driever & Nüsslein-Vollhard, Nature 337 138 (1989).
Bicoid protein also has the exponential
gradient one expects from a maternally
deposited morphogen!
However things are a little more
complicated than that – Hunckback is
expressed too precise in order to just be
determined by a Wolperian Bicoid...
Houchmandzadeh, Wieschaus and Leibler, Nature 415, 798 (2002)
Furthermore, the boundary is always in
the middle of the embryo irrespective of
ist size – this would not be expected
from an exponential gradient, which sets
a length scale.
On with the development of the fly…
During
metamorphosis
the imaginal
discs turn into
the proper
organs for
example the
wing is folded
out from the
wing disc
How does this influence the setting of scales
and coordinates in the wing disc, i.e. How is
the later shape of the wing encoded in this?
Imaginal discs also exist for eyes and legs
Expressing the 'wrong' genes in the leg disc
leads to legs with eyes