(notes from a 1994 copy of Molecular Biology of the Cell, a cheeky Russian has posted all images (and russian text) from the textbook here.
Geometric Strcture in the Early Vertebrate Embryo
The head to tail axis (anteroposterior)is already defined in the un-fertilized egg, however the back to stomach (dorsoventral) axis of the fertilized egg are only defined by where the sperm enters the cell. Roughly the sperm enters the egg around about your belly button (or rather causes your belly button to appear there). This is a clear data point in the nature/nurture debate - which way up you are is defined by the point where a sperm first touches the egg, a very chaotic event.
After a while we have a bunch of cells packed into a membraney sack. The shape they make is an interesting one - basically packed spheres within a larger spherical shell. Space subdivision based on membrane tension, rather than distance-to-a-point.This is very similar to soap bubble patterns. There are equations defining their shape at their boundaries, (the link is worth following for the pretty renders of bubbles). Something similar shows up up in weighted Voronoi tesselations as well.
Sodium is pumped into space between the cells, and via osmosis water follows. This forms a single cavity with a cruchy shell of cells. This leaves room for the wonderfully titled gastrulation, a process, it seems, whereby an arse appears and grows into a mouth. (This explains a lot about what comes out of people's mouths). Seriously - an indentation grows that forms the anus, then continues up to create a mouth. This shapes the cell into a torus around the nascent digestive system.
But where does this indentation come from and how is it controlled? A homogeneous structure suddenly creates this balstopore lip that becomes a digestive system. If you splice a second lip into a developing creature, both digestive systems grow and you end up with something non too pretty:-
This lip was one of the original organizer features documented and has the name Spearmann's Organizer. It's initial formation seems to be a result of regulative development (several cell movements in combination with morphogenic fields) and it goes on to control a lot of important growth functions in early embryos.
The two extremes that define development.
- Mosaic development - pattern of the body determined by features of the egg
- Regulative development - body determined by cell-cell interactions after fertilization
- When certain types of cells are adjacent, new cell-division behaviours can be turned on. This induction can happen several times to build up layers of different cells as the adjacency changes. Based on the concentrations of morphogens, cells can develop in different directions. Cell age also has an effect, older cells can behave in different ways to new cells.
i) two adjacent regions of cells
ii) new cell type induced by adjacency
iii) strata of cells via induction
ii) new cell type induced by adjacency
iii) strata of cells via induction
- The concept of function calls appears- "in this way the final specification of how a limb cell should behave is built up combinatorially; first it is supplied with information as whether it is to be a leg or wing then signals within the growing limb bud specify more fine-grained components of positional value, reflecting the precise position within the limb". So a programmer might say that values have been curried into the code for each part of the limb. You can see this in an experiment - if the tip of a embryonic chicken's foot is transplanted onto the end of the wing, you get a wing with a toe on the end; that is the tissue has already been curried (fated) as part of a leg, but doesn't know which part it is yet. (I wish computer science involved experiments like that - I mean just to spend the afternoon splicing bits between embryos is more excitement than the entire cs dept gets in a year, perhaps I should start a wet-lab in one of the terminal rooms that people never use, how about this one mixing up cells in an embryo, just to see what happens!).
- Cockroaches show another pattern - the parts of their legs seem to know where they are in the sequence, somehow they know their positional values. Through a process called intercalation any missing (ie a mid-portion of leg removed in an experiment) parts are eventually grown back. There's an idea for geometry deformation here - if you have a house, and stretch out a wall sensible house-parts should grow to fill in the space (much like mueller's 2006 paper) .
Linear animals - built end to end, easiest thing to encode for & follows digestive system. makes HOX etc... genes feasible?
- "Programmed death A C. elegans hermaphrodite generates 1030 somatic cell nuclei in the course of its development, but 131 die" - programmed cell deaths, cells that are "fated" to die. Is it possible for a system to have anti-features? features that cause something to disapear?
- Cells use a system of morphogenic fields to control features:
For example if you want a feature in the middle of an organism, cells should be programmed to transform in that way if the concentration of red and blue (in the above diagram) are identical. Most of these morphogens are unutterable TLAs, but their production and effects are quite relevant. Experiments that showed these principles included taking a fly egg (Drosphila) and removing some of the fluid containing the morphogens from the head end leading to a fly without a head. If you stick some arse-morphogentm in place of the head field, you get a fly with two sets of abdominal segments.
These fields would be rather robust when dealing with geometric features (if disrupted the system can re-organize itself) and may well prove to be well suited to procedural geometry that adapts to new features. The field effects could also be simulated using Voronoi-like arangements (I'm a bit hooked up on V. diagrams if you haven't noticed).
These fields can be seen as giving input to the growth-algorithm. They certainly solve the problems of symmetry in simple grammars (since diffusion is equal in all directions). There are several techniques that seem to be used - differentiating features by field strength or using a combination of fields, each producing another one -
- A function of another field strength.
- Equal strength of a number of other fields
- Orientation of the field (use the local field gradient for some function).
- Another technique is shown by the evaluation of "pair -rule" genes. A number of genes(hairy, even-skipped, paired, fushi-tarazu) of different lengths, are activated at intervals of two "segments". Different start-locations for the genes are apparent, and in combination (boolean operations - and, or, not, xor etc...) they can build more patterns.
This is really the idea expressed in Muller's 01 paper, that is used in 2D to positions windows on a façade (a boolean union of 2D pulse functions).
- If we suddently drop down to later in the development cycle (biologists don't seem to know what goes on between), there is a technqiue for producing occasional features called Lateral inhibition.
As in i) above all the cells start of with the same concentration of signal. Cells near those with a larger signal stop signalling, the result iii) is that we end up interspersed pattern. In this example each of the selected cells then becomes a mother cell to a clutch of hair-cells, while the remaining cells carry on as normal to become skin. The more complex patterns of stimulation/inhibition using morphogens are best described by Turing (free via the Turing institute).
Final thoughts: how much of this is suitable for algorithmic control? for artist control? the design certainly feels like it comes from the transcend, and is totally uncontrollable, unplannable. If any technique proves to be too complicated for an artist, then morphogenic fields become as good as any? However my first attempt at creating cell membrane using morphogenic fields had positive results in 3 hours -