Download Lecture V. Spatial organization in cells and embryos

Spatial organization
in cells and embryos
Robustness, bistability, and size
control
Marc W. Kirschner
Lecture V
April 7, 2005
Alan Turing’s seminal paper in (1952) , The chemical basis of
morphogenesis. Phil. Trans. B. Royal Society 237, 37-42, showed
that auto-activation and long range inhibition coupled with
diffusion could give rise to many different patterns. The major
problem he identified was the breakdown of symmetry.
Turing considered two cells, initially identical making two
morphogens, X and Y. He wrote:
dX/dt = 5X-6Y +1 (+diffusion) D=0.5
dY/dt = 6X-7Y +1 (+diffusion)
1
X
X
Y
Y
D=4.5
2
He points out that if both cells are identical then there is no concentration
difference and no differential between the cells.Assuming that the concentration is
X=1 and Y=, then the rate of production of both will be 0. However if the
concentration of X1 were 1.06 and X2 were 0.94; and similarly Y1= 1.02 and Y2 =
0.98, then the situation would be different. Cell 1 would produce the X
morphogen at a rate of 0.18 and Y at 0.22. This will produce a difference in the
diffusional flow of the two morphogens and the cells will exponentially become
more and more different in X and Y.
Hans Meinhardt and Alfred Gierer proposed a very general equation
for morphogenesis:
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Where a is an activator and h is an inhibitor. This is like the Turing example
since a is autocatalytic but is also negatively regulated. It is controlled by a
long range antagonist. Stochastic variation will produce patterns.
http://www.eb.tuebingen.mpg.de/dept4/meinhardt/periodic.html
http://www.eb.tuebingen.mpg.de/dept4/meinhardt/periodic.html
This generates fine patterns but what are the real
mechanisms used in development? (Hint: They are
not the same as the Gierer-Meinhardt equations.)
In Drosophila the anterior-posterior and dorsal ventral axes are set up independently.
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In the D/V axis a gradient of Dpp ( a member of the TGF-b
family). The highest concentration of Dpp forms the
extraembryonic nutritional tissues, the lowest forms mesoderm.
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The full circuit for generating the Dpp gradient is more complex.
The underlying question is how does one get discrete territories of
differentiation rather than graded territories, what are the spatial and
robustness requirements for getting the proper response, what is the
requirement of accurate initial localization of components?
The full circuit requires the following players:
1.
Dpp (decapentapalegic) which is transcribed in the dorsal half of the embryo.
2.
Sog (short gastrulation) which is transcribed in the next 40%. It binds Dpp and
inhibits it but has other important properties.
3.
Tld (tolloid), a protease that cleaves the dpp-sog.
4.
Scw (screw) another TGF-b molecule which is needed for complete response.
5.
Tsg (twisted gastrulation) a protein that makes a tripartite complex with sog and
dpp and blocks the interaction between dpp and its receptor.
6.
Tkv and Sax, are receptors for Dpp and Scw and are expressed globally.
Dpp
Tld
Tsg
Dpp
Scw,, Tkv, Sax
Sog + Tsg
Sog + Tkv
signal
Scw + Sax
Sog•Tsg•Dpp
Tld
Dpp
The robustness of the gradient measured with and anti PhosphoMad antibody.
Goes from dorsal 40%
to dorsal 10%
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Robustness to heterozygosity
Robustness to other conditions
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Nature 419 2002 p306
Quic kTime™ and a
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Their approach was to to take the basic features of the model
and then estimate the robustness by varying parameters.
The model assumes:
1. that neither Scw nor Dpp diffuse at all unless complexed to
Sog
2. That tld cleaves sog when complexed to Scw or Dpp
3. That tld does not cleave sog when not complexed
4. That receptors are everywhere present
5. The model only deals with either Dpp or Scw
X[Sog-Scw]
In these equations there is a diffusional term for sog, sog-scw,
and scw but the diffusion of scw is very minimal.
X[Sog-Scw]
In these equations there is a diffusional term for sog, sog-scw,
and scw but the diffusion of scw is very minimal. There is a
binding term to the receptor or other non-specific binding
that is governed by kb
X[Sog-Scw]
In these equations there is a diffusional term for sog, sog-scw,
and scw but the diffusion of scw is very minimal. There is a
binding term to the receptor or other non-specific binding
that is governed by kb. There is an unbinding term governed
by k-b.
X[Sog-Scw]
In these equations there is a diffusional term for sog, sog-scw,
and scw but the diffusion of scw is very minimal. There is a
binding term to the receptor or other non-specific binding
that is governed by kb. There is an unbinding term governed
by k-b. There is a destruction term of sog when sog is free
(a), and (l), when it is complexed with scw.
X[Sog-Scw]
These equations can be solved approximately for steady state
conditions where the time dependence vanishes. As
simplifications based on experimental evidence that in the absence
of Sog, DBMP = 0, we can set that equal to zero. Also we can
assume the binding is irreversible. The resulting equation is:
0 = 2 ([Scw]-1) - 2lb2 ;
Where lb = 2DSog/kb
At high Scw this reduces to a simple distribution around the dorsal
midline
[Scw(x)] = lb2/ x2
These equations can be solved approximately for steady state
conditions where the time dependence vanishes. As
simplifications based on experimental evidence that in the absence
of Sog, DBMP = 0, we can set that equal to zero. Also we can
assume the binding is irreversible. The resulting equation is:
0 = 2 ([Scw]-1) - 2lb2 ;
Where lb = 2DSog/kb
At high Scw this reduces to a simple distribution around the dorsal
midline
[Scw(x)] = lb2/ x2
In this model Sog diffuses from the ventral side, encounters Scw in the
dorsal region and transports it dorsally. In the dorsal region the Sog is
destroyed by Tld releasing Scw, where it binds nearly irreversibly to its
receptor. This process of transport, degradation of the carrier, and deposit on
the receptor continues to transport Scw dorsally and most of the deposit
occurs at the dorsal midline where the levels of Sog are the lowest.
The rest of the work by Barkai’s group tested the robustness of this
network for varying parameters. They found that many
processes gave non-robust networks but that what was most
important is that cleavage of Sog required a complex with Scw
and that it was only the complex of Sog-Scw that was broadly
diffusible. They also derived a more complex model with the
following properties:
1. Dpp and Scw both behave in similar ways.
2. Sog can bind Dpp and Scw when they are bound to their
receptors
3. Dpp binding to Sog requires the additional protein Tsg, which is
present in the dorsal half of the embryo. This distinguishes Scw
and Dpp, which are transported differently to the dorsal midline
What have we learned?
• The sharpening of the dorsal expression of Dpp and Scw
starts with a D/V asymmetry. This is a means of refining
that asymmetry. This is a common situation, patterning is
usually a set of nested specifications unlike Turing.
• The mechanisms used here are quite different than the ones
considered by Turing and Gierer-Meinhardt. This model
uses facilitated diffusion, selective proteolysis, and
complex formation.
• Robustness as a criterion may be weak, since we do not
know exactly what the conditions are. It must be tested
experimentally, as it was partially done by Eldar and
Barkai.
Spatial bistability is not so simple
Nature (2005) 434 p229
Barkai’s group argued for a certain kind of robustness under modeling
conditions. Yet the conditions are not that well defined. For example they found
that the concentration of Dpp was not that robust unless the concentration was
that much higher.
Chip Ferguson considers other aspects of the signaling system that involve
internal circuitry in the cell that help produce a kind of bistability. The bistability
concerns the sharpening of the Dpp domain or more accurately the Dppdependent transcription into a small region of the dorsal midline.
There is a progressive sharpening of pMad expression (downstream
of dpp and scw)
The gene Tsg is clearly important. Tsg is important for transport of
Dpp as shown below
Sog minus
Tsg minus
But Tsg is important for another purpose. Without Tsg, Dpp does not
bind to the receptor. So to the model of Barkai we have to add
another feature: Tsg mediates Dpp binding to the receptor.
Scw and Dpp are not independent. This is not just another seeming
redundant or partially redundant pathway. Dpp binding requires that
Scw be present at the same place.
Finally the binding of Dpp to its receptor requires gene expression as
part of a positive feedback loop acting to facilitate Dpp binding!
The More Realistic Model
The More Realistic Model
Binding
The More Realistic Model
X is a transcriptional target
General conclusions
• Reaction-diffusion equations are easy to write and
can easily generate many patterns.
• Real biological systems are always very different
than Turing or Gierer-Meinhardt.
• Robustness is easily over interpreted; it must be
evaluated at the level of the whole organism.
• Regulation involves much more than transcription,
e.g. Protein degradation, phosphorylation, binding,
spatial regulation.
• Levels of regulation are not easily separated