spatial organization in cells and embryos

Spatial organization in cells and embryos

Robustness, bistability, and size control

Marc W. KirschnerLecture 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)

dY/dt = 6X-7Y +1 (+diffusion)

X

Y

X

Y

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.

D=0.5

D=4.5

1 2

Hans Meinhardt and Alfred Gierer proposed a very general equation for morphogenesis:

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are needed to see this picture.

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


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-family). The highest concentration of Dpp forms the extraembryonic nutritional tissues, the lowest forms mesoderm.

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- 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.

TsgTld

Scw, Tkv, Sax,

Sog + Tkvsignal

Scw + Sax

Sog + Tsg

Sog•Tsg•Dpp DppTld

Dpp

Dpp

The robustness of the gradient measured with and anti Phospho-Mad antibody.





Robustness to heterozygosity



Robustness to other conditions



Nature 419 2002 p306

Goes from dorsal 40% to dorsal 10%

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

Sog2. That tld cleaves sog when complexed to Scw or Dpp3. That tld does not cleave sog when not complexed4. That receptors are everywhere present5. 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 (, and (, 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 = ([Scw]-1) - 2lb2 ;

Where lb = 2DSog/kb

At high Scw this reduces to a simple distribution around the dorsal midlineScw(x)] = lb

2/ 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 = ([Scw]-1) - 2lb2 ;

Where lb = 2DSog/kb

At high Scw this reduces to a simple distribution around the dorsal midlineScw(x)] = lb

2/ x2In 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

receptors3. 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 Dpp-dependent 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


Binding

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

spatial organization in cells and embryos

Documents

gradient of dpp

dpp gradient

dpp decapentapalegic

highest concentration

x morphogen

concentration difference

different patterns

dorsal half