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Overview 111111111111111111111333333333333333333333222222222222222222222 I Introduction II Cartesian genetic programming Cell Programming: French III Developmental Cartesian genetic programming IV Evolving growing 2-D maps Flags/Boolean Circuits A. How cells and chemicals are represented B. How a cell program is encoded into a genotype C. experimental parameters D. Tasks for the cellular maps V Experiment and results A. Analysis of the genotype Murray Bratland CPSC607 VI Discussion February 3, 2005 Introduction Introduction (con’t) • Life: single cell � complete organism • Two reasons for studying cell-related development: 1. help understand developmental biology Cell: unit of life (1013 in humans) • 2. see if developmental approaches can help solve computer – self renewal (life and death cycle), self repair, adaptation to/interaction with the environment science problems • Developmental biologists’ view: – How do cells self regulate? Two questions being asked: – What is the underlying structure? – If each cell has the same program, how can complex structures be • Computer Scientists’ view: created? – cell = mini robot that can: eat food, interact with the environment, and – How can self-regulated structures be made? replicate. – What developmental processes are incidental? fundamental? – What is the underlying structure of cell processes? Cartesian Genetic Programming CGP (con’t) (CGP) The 6 steps in chromosome evolution/fitness 3. Generate 5 chromosomes randomly to form the population 4. Evaluate the fitness of all the chromosomes on the population The above drawing is an example of a Boolean Circuit where f0 is 5. Determine the best of all the chromosomes in the population addition and f1 is multiplication 6. Generate 4 more chromosomes (offspring) by mutation the current_best 7. The current_best and the four offspring become the new 001102113… x4 + 2x3 + x2 + x population 001112113… 8. Unless stopping criterion reached return to 2. Note: “+” evolutionary strategy; mutation/duplication exercised Graph resulting from above nodes

Developmental CGP Evolving growing 2-D maps • 4 Inputs to cell: – 2 connections (A,B) • Plan: create a 2-D world of cells of different types, each with – a function (F) identical GT – it’s position (P) • 4 Outputs from cell: – 2 new connections (A',B') – new function (F ' ) – Divide? Y/N (D) A “cell” – Outputs produced from the program inside the node (previous) – Goal: evolve smaller programs and use them to create larger ones How cells and chemicals are How cells and chemicals are represented represented (con’t) • The GT represents a Boolean circuit : maps input -> • Chemicals: 8-bit binary code output 4 types: dead (none), blue, white, red • Cell sees (Clockwise): • Diffusion rule ensures dead cells will not alter chemical landscape – Its own state: 2 bits (cell type) + 8 bits (chemical) (cij)new = 1/2(cij)old + 1/16 � k,l � N(ckl)old – state of 8 neighbours: 2 bits x 8 – chemical amount of 8 neighbours: 8 bits x 8 • Program cycle: • Cell determines (Counterclockwise): scan a cell – amount of chemical to produce (8 bits) growth/differentiation/death – Whether to live or die (1 bit) update landscape – If it should change into a different cell (2 bits) – how it will grow (8 bits) • (1 = blue, 2 = red, 3 = white cell, 0 = empty/dead • Later cells overwrite previous cells, therefore, bias to bottom right 72 68 44 cell) cells 84 76 64 92 83 75 How cells and chemicals are How a cell program is encoded represented (con’t) into a GT • GT = 400 integers (only ~ � the nodes are active) • Three questions of interest: – Each group of 4 integers represents one of four 2:1 multiplexers and its three connections – “ 2:1 multiplexer ” – 3-input Boolean logic gate 1. How can collections of independent cells interact/coordinate • i.e. f (A,B,C) = A.C + B.C = (A AND NOT C) OR (B AND C) to build an organism? • Experimental Parameters 2. What is importance of direct cell interaction and global – Algorithm used to evolve the GTs described previously chemical signaling? – Mutation rate = 1% / generation – 30,000 generations 3. How can we regulate growth?

French Flag analogy1 Tasks for the cellular maps FRENCH FLAG (Lewis Wolpert, 1998) MODEL • Goals: 1. Construct a French Flag through cell programmed evolution - condition: must always look like a French Flag 2. Grow French Flag to specified size and remain at that size • How will the cell/flag map behave when damaged? When cells are translated to other regions? • Set up: place one initial cell on an existing chemical map • Success is measured as “ Fitness ” – at random generations, compare current map to desired map; sum those cells in agreement 1Gilbert, S.F. (2003) Experiments 1. Create the French Flag with no deformations Experiments and results 2. If remove parts of the French Flag, what will happen? 3. If cut a large hole in the French Flag at iteration 9, what happens? 4. If cut the French Flag diagonally at iteration 9, what happens? 5. How can the French Flag be made to grow to a set size and stop? (growth, stasis) 6. What happens if a cell’s initial chemical level is set to zero? 7. Extra: Want to obtain a regular series of spots 1. Create the French Flag with Experiment 1 (con’t) no deformations • Requirements: cells develop medium flag at iteration 7 and large flag at iteration 9.

Experiment 1 (con’t) 2. If remove parts of the French Flag, what will happen? • Remove White and red cells at iteration 9 and continue to grow map • The blue region tries to grow into French Flag again (FAILED) rather than just making a blue map 3. If cut a large hole in the French Experiment 2 (con’t) Flag at iteration 9, what happens? • Map at 15 has red section identical to that of original map • Cells try to rebuild map 4. If cut the French Flag diagonally Experiment 4 (con’t) at iteration 9, what happens? • Blue region is not cut • This region returns to “normal” (Looks almost like original map) • Cells try to rebuild map

5. How can the French Flag be made to grow to a set size and stop? (growth, stasis) • Note that chemicals help slow down growth “naturally,” but do not stop growth • Note! Vertical stripes maintained to iteration 29, even to 46, though looks “interesting” Iteration 22 Iteration 46 6. What happens if a cell’s initial Experiment 6 (con’t) chemical level is set to zero? • Cells still grow at same rate as unaltered map • Iterations 0->2 exact same as unaltered growth • Forms triangle • Shows chemical influence is important for high fitness • Compare: with chemicals: average fitness: 438 dev 26 without chemicals: average fitness: 400 dev 14 7. Extra: Want to obtain a Results Summary regular series of spots • Perfect possible fitness = 196 (needed by iteration 5) • Can grow French Flag with given parameters • 3/10 obtained a perfect score (different ways to do so) – Average fitness = 191 • Self-repair works only on minor deformations • without chemical influence the result was not favourable – Best fitness = 192 – Average fitness = 182 • Self-repair attempted in all cases • Chemical landscape important to development • Ability to use underlying chemical structure to produce “other” structures

Problems Future Work • Cell update procedure may cause problems with end result • Work on a better self-repair mechanism may allow the – Cells can override one another, in logical course French Flag to undergo more recognizable repair – DOESN’T HAPPEN IN LIFE!! – Application: Self-repairing circuits • This can perhaps be fixed by adding in GT judgment on how to grow based on chemical demands of neighbouring cells • Chemotaxis: add a point where cells could grow to • In this series of experiments all cells are stem cells instead of simply “outward” – Could create an experiment so most cells are not stem cells, with introduction of a rare few stem cells to evolve the map – Or, allow a number of different chemicals to be emitted by cells • Try starting with multiple seed cells in initial map • This allows for orientation-independent fitness function, if possible • This would allow for electronic circuit design, since orientation doesn’t matter (just function) • Debate: Direct encodings versus Developmental • Bias in growth: all 8 neighbouring cells must be zero for zero growth encodings? to occur 0 0 0 0 76 0 0 0 16 References and interesting Web pages 111111111111111111111333333333333333333333222222222222222222222 • Morgan, D.E. (Ed.). (2003). On Growth, Form and Computers: Chapter 15 : by Miller, J., & Banzhaf, W. (2003). London: Elsevier Academic Press. Gilbert, S.F. (2003). Developmental Biology, 7th ed. Sunderland, • Questions? Massachusetts: Sinauer Associates, Inc. • Wolfgang Banzhaf’s homepage: http://www.cs.mun.ca/~banzhaf/ • Jullian F. Miller’s Web page: http://www.cs.bham.ac.uk/~jfm/french-flag/