Using an Artificial Regulatory Network to Investigate Neural Computation

Transcription

1 Using an Artificial Regulatory Network to Investigate Neural Computation W. Garrett Mitchener College of Charleston January 6, 25 W. Garrett Mitchener (C of C) UM January 6, 25 / 4

2 Evolution and Computing Section Evolution and Computing W. Garrett Mitchener (C of C) UM January 6, 25 2 / 4

3 Evolution and Computing Computation: sequential register machine Short list of fixed-width registers Large external memory Each instruction makes small modification from Waldspurger & Weihl 994 W. Garrett Mitchener (C of C) UM January 6, 25 3 / 4

4 Evolution and Computing Computation: Expression trees Expression tree Evaluated by reductions = power multiply 4 add W. Garrett Mitchener (C of C) UM January 6, 25 4 / 4

5 Evolution and Computing Computation: Minimalist syntax John gave Fred a book TP John T' [tense=past] VP John V give vp Fred v' give v give book W. Garrett Mitchener (C of C) UM January 6, 25 5 / 4

6 Evolution and Computing Computation: Minimalist syntax Who gave Fred a book? CP C' who give[past] TP who T' [tense=past] VP who V give vp Fred v' give v give book W. Garrett Mitchener (C of C) UM January 6, 25 6 / 4

7 Evolution and Computing Bio-computing: Genes and transcription regulation laci repressor laci disabled by lactose lacz enzyme lacy laca lactose lac operon galactose glucose Molecules in solution: ions, proteins, DNA, RNA,... Many simultaneous reactions W. Garrett Mitchener (C of C) UM January 6, 25 7 / 4

8 Evolution and Computing Biological Computation: Action potentials Electrical pulses sent via ions, neurotransmitters Detect coincidences, crossing of threshold Vast neural networks, active cardiac tissue W. Garrett Mitchener (C of C) UM January 6, 25 8 / 4

9 Utrecht Machine Section 2 Utrecht Machine W. Garrett Mitchener (C of C) UM January 6, 25 9 / 4

10 Utrecht Machine Utrecht Machine: State patterns: transcription factors (integer) activation: molecule count (integer) p A[p] W. Garrett Mitchener (C of C) UM January 6, 25 / 4

11 Utrecht Machine Utrecht Machine: Instructions j : A[p switch ] θ A[p p ] A[p down ] j: instruction number p switch : switch pattern θ: threshold p p : pattern to increment If the activation of p switch is at least θ, add one to the activation of p p and subtract one from the activation of p down. p down : pattern to decrement W. Garrett Mitchener (C of C) UM January 6, 25 / 4

12 Utrecht Machine UM Example: NAND : A[] A[] A[7] : A[] A[6] A[7] 2: A[2] A[6] A[7] 3: A[4] A[7] A[6] 4: A[5] A[7] A[6] Input via A[4] and A[5] utput is A[6]? 3 Stop when A[] 4 W. Garrett Mitchener (C of C) UM January 6, 25 2 / 4

13 Utrecht Machine UM Example: NAND : A[] A[] A[7] : A[] A[6] A[7] 2: A[2] A[6] A[7] 3: A[4] A[7] A[6] 4: A[5] A[7] A[6] Input via A[4] and A[5] utput is A[6]? 3 Stop when A[] 4 A[s] θ A[p p ] A[p down ] θ p up s θ p down W. Garrett Mitchener (C of C) UM January 6, 25 2 / 4

14 Utrecht Machine UM Example: NAND : A[] A[] A[7] : A[] A[6] A[7] Input NAND 2: A[2] A[6] A[7] 3: A[4] A[7] A[6] 4: A[5] A[7] A[6] Input via A[4] and A[5] utput utput is A[6]? 3 Stop when A[] Show only efficacious genes and arrows W. Garrett Mitchener (C of C) UM January 6, 25 2 / 4

15 M P P nm ng U S ng P og M nm 65.9 st position nm 2 nd rd P og P og G nm (hydrophobic) P nm Utrecht Machine Biological genetic code H H 3C H H 2N H 2N H 3 C H 2N H H 2N H 2N H 2N H 2N H 2N H CH 3 CH 3 H 2N H H 2N H Glutamic acid Glu H H Aspartic acid Asp H Alanine Ala Valine Val Arginine Arg Serine Ser Lysine Lys H Asparagine Asn H H 3 C H Threonine Thr S H 2N Methionine Met H 2N H V H Glycine Gly A G UC U CA R S K N G A C U G A D UC AG A G UCA G UCA G UCA A GUC C U C U G A A C G G A U Phenylalanine Phe E G F L S U G C A A G U C G U A C C UG G A A CU GA CU T MW = 49.2 Da M I Isoleucine Ile H 2N H 3 C CH 3 HN U C H R NH NH 2 H 2N Q A G Y G U CA G U C A G U C H Arginine Arg H 2N H Leucine Leu P C W L H 3C H 3C Stops H H 2N H Serine Ser Tyrosine Tyr Cysteine Cys Stop H 2N Tryptophan Trp Leucine Leu Proline Pro H Histidine His Glutamine Gln H N H NH H 3C H 3C NH NH 2 HS NH H 2N Basic Acidic Polar Nonpolar S - M - P - U - nm - og - ng - H 2N H 2N H 2N H 2N H 2N Modification Sumo Methyl Phospho Ubiquitin N-Methyl -glycosyl N-glycosyl H H amino acid H H H H H st base U C A G 2nd base U C A G UUU UCU UAU UGU U UUC Phenylalanine UCC UAC Tyrosine UGC Cysteine C UUA UCA Serine UAA Stop (chre) UGA Stop (pal) A UUG UCG UAG Stop (Amber) UGG Tryptophan G 3rd base CUU CCU CAU CGU U CUC Leucine CCC CAC Histidine CGC C CUA CCA Proline CAA CGA Arginine A CUG CCG CAG Glutamine CGG G AUU ACU AAU AGU U AUC ACC AAC Asparagine AGC Serine C Isoleucine AUA ACA Threonine AAA AGA A AUG Methionine ACG AAG Lysine AGG Arginine G GUU GCU GAU GGU U GUC Valine GCC Alanine GAC Aspartic acid GGC Glycine C GUA GCA GAA GGA A GUG GCG GAG Glutamic acid GGG G W. Garrett Mitchener (C of C) UM January 6, 25 3 / 4

16 Utrecht Machine Utrecht Machine: Genetic code, majority-of-three Two robust codons: decodes to decodes to Takes two substitutions to change interpretation Six fragile codons:,, : Decode to,, : Decode to ne substitution can change W. Garrett Mitchener (C of C) UM January 6, 25 4 / 4

17 Utrecht Machine Utrecht Machine: Genetic code Genome & instructions : A[] A[] A[7] : A[] A[6] A[7] 2: A[2] A[6] A[7] 3: A[4] A[7] A[6] 4: A[5] A[7] A[6] W. Garrett Mitchener (C of C) UM January 6, 25 5 / 4

18 Utrecht Machine UM: Point substitutions W. Garrett Mitchener (C of C) UM January 6, 25 6 / 4

19 Utrecht Machine UM: Deletions W. Garrett Mitchener (C of C) UM January 6, 25 7 / 4

20 Utrecht Machine UM: Duplications W. Garrett Mitchener (C of C) UM January 6, 25 8 / 4

21 Utrecht Machine UM: Crossover W. Garrett Mitchener (C of C) UM January 6, 25 9 / 4

22 Utrecht Machine Communication problem setup Input Sender Receiver utput W. Garrett Mitchener (C of C) UM January 6, 25 2 / 4

23 Utrecht Machine Example solution: Sample Run 47, agent Input Sender Receiver utput W. Garrett Mitchener (C of C) UM January 6, 25 2 / 4

24 Utrecht Machine Selective breeding Breed 2 children from highest Breed children from whole population New population = 2 old agents with the highest rating + 3 new agents... W. Garrett Mitchener (C of C) UM January 6, / 4

25 Utrecht Machine Evolutionary overview 8k 6k Maximum score of first n agents created as a function of n 8 32 V 843 4k 2k k 23k W. Garrett Mitchener (C of C) UM January 6, / 4

26 Utrecht Machine Running to saturation k 7k 6k 2 5k 4k 3k 2k k ne perfect solution takes many generations to saturate the population. V 843 W. Garrett Mitchener (C of C) UM January 6, / 4

27 Utrecht Machine Implicit selection for robustness First perfect solution found 2 Runs to saturation 3 Competition for 2 survivor slots 4 Favors agents whose offspring are more likely to have perfect scores 5 favors robustness against mutation and crossover W. Garrett Mitchener (C of C) UM January 6, / 4

28 Utrecht Machine Measuring robustness: Deleterious mutations Mutations that lower performance are deleterious Measure of robustness g = base genome with perfect score M(g) = all possible mutations G = set of genomes one mutation away from g G = { g m m M(g) } How many genomes in G score less than g? What fraction of genomes in G score less than g? W. Garrett Mitchener (C of C) UM January 6, / 4

29 Utrecht Machine Sample Run 43: Deleterious mutations frac del muts a. num genes b generations W. Garrett Mitchener (C of C) UM January 6, / 4

30 Sample Run 7: Synaptic Code Section 3 Sample Run 7: Synaptic Code W. Garrett Mitchener (C of C) UM January 6, / 4

31 Sample Run 7: Synaptic Code Sample Run 7: Synaptic Codes W. Garrett Mitchener (C of C) UM January 6, / 4

32 Sample Run 7: Synaptic Code Sample Run 7: Synaptic Codes Activation times: t, t, t, t W. Garrett Mitchener (C of C) UM January 6, / 4

33 Sample Run 7: Synaptic Code Sample Run 7: Synaptic Codes Activation times: t, t, t, t Synaptic timing gap: STG = min, t t W. Garrett Mitchener (C of C) UM January 6, / 4

34 Sample Run 7: Synaptic Code Sample Run 7: Synaptic timing gap distribution Fraction of perfectly scoring agents with STG of, 2, 3 as a function of generation number W. Garrett Mitchener (C of C) UM January 6, 25 3 / 4

35 Sample Run 47: Simplification, Redundancy, Codon bias Section 4 Sample Run 47: Simplification, Redundancy, Codon bias W. Garrett Mitchener (C of C) UM January 6, 25 3 / 4

36 Sample Run 47: Simplification, Redundancy, Codon bias Sample Run 47, agent Input 9 Sender Receiver 3 utput First perfect solution. W. Garrett Mitchener (C of C) UM January 6, / 4

37 Sample Run 47: Simplification, Redundancy, Codon bias Sample Run 47, agent Input Sender Receiver utput Dangerous extra link is gone W. Garrett Mitchener (C of C) UM January 6, / 4

38 Sample Run 47: Simplification, Redundancy, Codon bias Sample Run 47, agent Input 9 Sender 3 Receiver utput Redundancy appears W. Garrett Mitchener (C of C) UM January 6, / 4

39 Sample Run 47: Simplification, Redundancy, Codon bias Codon bias two robust codons six fragile codons Each gene has 22 codons If uniformly random expect 5.5 robust codons per gene If robustness favored expect more Consider genes with 6 or more robust codons frac eff robust frac ineff robust generations a b W. Garrett Mitchener (C of C) UM January 6, / 4

40 Sample Run 59: Genome Rearrangement Section 5 Sample Run 59: Genome Rearrangement W. Garrett Mitchener (C of C) UM January 6, / 4

41 Sample Run 59: Genome Rearrangement Sample Run 59: First perfect solution, generation 36 Sender Input 9 4 Receiver utput = inefficacious. = part of sender. = part of receiver. = part of both. W. Garrett Mitchener (C of C) UM January 6, / 4

42 Sample Run 59: Genome Rearrangement Sample Run 59: Perfect solution from generation 7 Input Sender 9 Receiver utput = inefficacious. = part of sender. = part of receiver. = part of both. W. Garrett Mitchener (C of C) UM January 6, / 4

43 Sample Run 59: Genome Rearrangement Sample Run 59: Perfect solution from generation 27 Input 9 2 Sender Receiver utput = inefficacious. = part of sender. = part of receiver. = part of both. W. Garrett Mitchener (C of C) UM January 6, / 4

44 Sample Run 59: Genome Rearrangement Sample Run 59: Genome rearrangement = inefficacious. = part of sender. = part of receiver. = part of both. W. Garrett Mitchener (C of C) UM January 6, 25 4 / 4

45 Sample Run 59: Genome Rearrangement Sample Run 59: Genome rearrangement = inefficacious. = part of sender. = part of receiver. = part of both. W. Garrett Mitchener (C of C) UM January 6, 25 4 / 4

46 Sample Run 59: Genome Rearrangement Sample Run 59: Genome rearrangement = inefficacious. = part of sender. = part of receiver. = part of both. W. Garrett Mitchener (C of C) UM January 6, 25 4 / 4

47 Sample Run 59: Genome Rearrangement About me Web site: W. Garrett Mitchener (C of C) UM January 6, 25 4 / 4