Evolution of the morphology and patterning of artificial embryos: scaling the tricolour problem to the third dimension - supplementary materials

This page contains supplementary materials for the ECAL 2009 paper by Michal Joachimczak and Borys Wrobel
We are in the Evolutionary Systems Lab, Institute of Oceanology, Polish Academy of Sciences.
If you have any questions or comments, don't hesitate to contact me: mjoach ( at ) gmail . com

Contents:

  1. Paper overview
  2. Illustration of the diffusion model used in the system
  3. Development of best individual shown on Figure 4
  4. Development of individuals evolved for modified versions of the problem (Figure 6)
  5. Individuals that vary cell sizes
  6. Related work
  7. Reference/BibTeX

1. Paper overview

Abstract: We present a model of three-dimensional artificial embryogenesis where multicellular embryo develops controlled by continuous regulatory network encoded in a linear genome. Development takes place in a continuous space, with spherical cells of variable size and is controlled by simulated physics. We apply genetic algorithm to the problem of simultaneous evolution of morphology and patterning into colour stripes and demonstrate how the system achieves the task by exploiting physical forces and using self-generated morphogen gradients.

We observe high degree of robustness to damage in evolved individuals and explore the limits of the system using more complex variations of the problem. We find that despite the increased complexity of three dimensional space and a flexible coding of the genome that requires from evolution to invent all necessary morphogens and transcription factors, the system remains highly evolvable.


2. Illustration of the diffusion model used in the system

To avoid processing diffusion on a 3D grid (which would be costly and would make developmental process sensitive to the offset between cells and the grid) we use a simplified diffusion model that attempts to capture some of the spatio-temporal aspects of diffusion. The concentration of a product diminishes with the distance from source and furthermore, information about the change in morphogen expression travels with a limited speed throughout the system. This is achieved by storing historic values of morphogen production at the source. When perceived concentration at some distant point in space is calculated, the larger the distance, the older value is used. Such system calculates morphogen concentrations only where it's needed (that is for each cell). Introducing limited speed of information propagation has only memory cost.

A changing gradient of morphogen density in space is shown on the figure below. This may not be immediately obvious as it is difficult to visualize gradients in 3D and there is no perfect method for that. What is seen below, are coloured gradients computed for selected points in the cubical area around the embryo, seen from an angle. For each point in space, a gradient is calculated and the vector is drawn. The length of the vector corresponds to the gradient, whereas its colour corresponds to the concentration. When nothing is perceived for a given point in space, no vector is drawn. As soon as expression starts, you will thus see a spherical halo of morphogen diffusing around the embryo. Switching on high quality and embigenning the video may be necessary to discern individual points.


An outburst of morphogen production in the embryo followed by quick degradation produces a wave of perceived concentration increase travelling throughout the system


3. Development of the best evolved individual (shown on Fig. 4 in the paper)

a) System setup

Two colour effector genes are used (red and blue), thresholded at 0.5 . Colours on screen are assigned so that no expression is drawn as white, i.e.

Colour Red effector Blue effector
White <0.5 <0.5
Red >=0.5 <0.5
Blue <0.5 >=0.5
Pink >=0.5 >=0.5

Target pattern is:

Small spheres seen on the pattern correspond to locations of cubical voxels, of each every is tested for being occupied by cell with correct colour expression pattern to compute fitness. The edge of the voxel is 3 times smaller than minimal cell size. Camera angle added only two emphasize that this is a 3D shape, an ellipsoid. For this particular experiment, embryos were allowed to contain 200 cells at max. Experiments from Fig. 6ab allowed maximum of 100 cells (which was faster, but usually gave lower best fitnesses).


The evolved regulatory network of this individual can be seen as PDF file. Note, that only connections with weights above threshold are drawn, as a very large number of low weight connections was obtained (and this is common in our system). We are currently investigating whether this actually hinders the evolutionary search or facilitate. Download figures for |weight|>1 and |weight|>2.



b) Developmental process

Developmental process, 300 steps, 20 fps, 200 cells (Fig. 4a)
Orientation of cell vectors during development (Fig. 3 in the paper),
cells were shrunk to make vectors clearly visible



c) Self generated gradient formation (Fig. 4bc) - cell colour shows expression of the given morphogen, gradient map shows its concentration in space (colour=concentration, vector direction=gradient)

Self generated gradient of positional information on the left side of the embryo
Self generated gradient of positional information on the right side



d) Expression of the red/blue colour genes (without thresholding) - blue-red colour map (expressions in the model can be only between 0 and 1)

Self generated gradient of positional information on the left side of the embryo
Self generated gradient of positional information on the right side



4. Development of individuals evolved for modified versions of the problem (Figure 6)

a) non-thresholded colour mode, two colour effector genes - red/blue

In this mode, the expression of colours is not thresholded, so ideally individual has to express red and blue external factors at the level of 1. This is more difficult as the sharp border between expression and no expression is hard to obtain - in thresholded mode it would be enough to simply express colour gene slightly above 0.5 at the colour border and slightly below next to it.

Target pattern is:

Colour is drawn as composite of appropriate effector expressions, i.e. RGB(255*red_expression,0,255*blue_expression)







Best individual #1 (Fig. 6a, middle)
Best individual #2 (Fig. 6a, bottom)



b) three colour effectors (red,green, blue) have to generate three colour areas

Again, a more difficult problem - 3 (thresholded) colour effector genes are used, an individual has to express correct gene in a given stripe and repress remaining two.

Target pattern is:

Colour is drawn as composite of thresholded effector expressions, i.e. RGB(255*(red_expression>0.5), 255*(green_expression>0.5), 255*(blue_expression>0.5))







Best individual #1 (Fig. 6b, middle)
Best individual #2 (Fig. 6b, bottom)



c) two colour effectors have to generate 4 colour areas

Here, two thresholded colour effectors (Red/Blue) were used to generate 4 stripes with all possible expression patterns.

Default colour palette is used, i.e. the lack of expression of both effectors is drawn white, simultaneous expression of both is seen as pink.

Target pattern is:








Best individual #1 (Fig. 6c, middle)
Best individual #2 (Fig. 6c, bottom)



d) multiple alternating stripes (Fig. 6d) 

Here, two thresholded colour effectors (Red/Blue) were used to generate alternating pattern of expressing one and repressing the other colour effector, in a manner similar to odd/even patterning genes in Drosophila development. 

Target pattern is:

Target - multiple stripes

Default colour palette is used., i.e. the lack of expression of both effectors is drawn white, simultaneous expression of both is seen as pink.








Best individual #1 (Fig. 6d, middle)
Best individual #2 (Fig. 6d, bottom)




5. Individuals that vary cell sizes

In the paper, we mention that one of the effectors that cells can use is the ability to set the size of daughter cell during division (diameter can be between 1 and 4 times of the default). This, however, cannot be seen for the best individual shown on Fig. 4 as its developmental process doesn't make use of this mechanism (although it has it available). Some of the individuals would however make use of it, as can be seen below.






Example individual that clearly uses cell size effector
"Evolution is always smarter than you" - this solution was found among best individuals, managing to obtain very high fitness despite rather disapointing complexity

6. Related work

Have a look at our earlier work on the evolution of 3D morphology based on the same model:

M. Joachimczak and B. Wrobel. Evo-devo in silico: a model of a gene network regulating multicellular development in 3D space with artificial physics. In S. Bullock, J. Noble, R. Watson, and M. A. Bedau, editors, Artificial Life XI: Proceedings of the Eleventh International Conference on the Simulation and Synthesis of Living Systems, pages 297-304. MIT Press, Cambridge, MA, 2008. BibTeX / RIS / CiteULike 
Videos from the paper are available.


Also, have a look at our follow-up work on the same GRN model, where it is used to control unicellular animats.

Also recommended, some excellent work on the French-flag model by other researchers; in two dimensions, but with a more complex model of cell shape (Cellular Potts Model), with online demos:

Knabe, J. F., Nehaniv, C. L. and Schilstra, M. J. Evolution and Morphogenesis of Differentiated Multicellular Organisms: Autonomously Generated Diffusion Gradients for Positional Information. In Artificial Life XI: Proceedings of the Eleventh International Conference on the Simulation and Synthesis of Living Systems, pages 321-328, MIT Press, 2008.

7. Reference/BibTeX

Evolution of the morphology and patterning of artificial embryos: scaling the tricolour problem to the third dimension. In: Proceedings of 10th European Conference on Artiļ¬cial Life (ECAL 2009), volume 5777 of LNCS, pages 33-41, Springer.
BibTeX / RIS /  CiteULike 



Last modified: July 2012