Case Study of Molecular Algorithm Design CMC12, - PowerPoint PPT Presentation

Case Study of Molecular Algorithm Design CMC12, Fontainebleau/Paris, August 2011 Gerd Gruenert, Gabi Escuela, Peter Dittrich, Thomas Hinze Friedrich Schiller University, Jena School of Biology and Pharmacy, Department of Bioinformatics Gerd Gruenert, Gabi Escuela, Peter Dittrich, Thomas Hinze – Uni Jena, Bio Systems Analysis Group 1

Word 2007 as Turing Machine? Gerd Gruenert, Gabi Escuela, Peter Dittrich, Thomas Hinze – Uni Jena, Bio Systems Analysis Group 2

Word 2007 as Turing Machine? Morphological Algorithms? Gerd Gruenert, Gabi Escuela, Peter Dittrich, Thomas Hinze – Uni Jena, Bio Systems Analysis Group 3

Exact Cover Problem Gerd Gruenert, Gabi Escuela, Peter Dittrich, Thomas Hinze – Uni Jena, Bio Systems Analysis Group 4

Exact Cover Problem X F Elements: X = {a,b,c,d,e} a Subsets: F = {A,B,C} A b B A = {a,d} c C B = {a,b} d C = {c,d,e} e Gerd Gruenert, Gabi Escuela, Peter Dittrich, Thomas Hinze – Uni Jena, Bio Systems Analysis Group 5

Exact Cover Problem X F Elements: X = {a,b,c,d,e} a Subsets: F = {A,B,C} A b B A = {a,d} c C B = {a,b} d C = {c,d,e} e Gerd Gruenert, Gabi Escuela, Peter Dittrich, Thomas Hinze – Uni Jena, Bio Systems Analysis Group 6

Exact Cover Problem X F Elements: X = {a,b,c,d,e} a Subsets: F = {A,B,C} A b B A = {a,d} c C B = {a,b} d C = {c,d,e} e Gerd Gruenert, Gabi Escuela, Peter Dittrich, Thomas Hinze – Uni Jena, Bio Systems Analysis Group 7

Exact Cover Problem X F Elements: X = {a,b,c,d,e} a Subsets: F = {A,B,C} A b B A = {a,d} c C B = {a,b} d C = {c,d,e} e Select Elements such that: ● All elements from X covered ● No element from X covered twice Gerd Gruenert, Gabi Escuela, Peter Dittrich, Thomas Hinze – Uni Jena, Bio Systems Analysis Group 8

Exact Cover Problem X F Elements: X = {a,b,c,d,e} a A b Subsets: B F = {A,B,C} c C d e A = {a,d} B = {a,b} C = {c,d,e} {B,C} is an exact set cover of X : Select Elements such that: ✔ X = B ∪ C, and ● All elements from X covered ✔ B ∩ C = ∅ ● No element from X covered twice Gerd Gruenert, Gabi Escuela, Peter Dittrich, Thomas Hinze – Uni Jena, Bio Systems Analysis Group 9

Exact Cover Problem X F Elements: X = {a,b,c,d,e} a A b Subsets: B F = {A,B,C} a b c d e c C A x x d B x x e A = {a,d} C x x x B = {a,b} C = {c,d,e} {B,C} is an exact set cover of X : Select Elements such that: ✔ X = B ∪ C, and ● All elements from X covered ✔ B ∩ C = ∅ ● No element from X covered twice Gerd Gruenert, Gabi Escuela, Peter Dittrich, Thomas Hinze – Uni Jena, Bio Systems Analysis Group 10

Brute Force Approach X F Rrrrrraar! a A b B c C d e Gerd Gruenert, Gabi Escuela, Peter Dittrich, Thomas Hinze – Uni Jena, Bio Systems Analysis Group 11

Brute Force Approach X F a A b B c C d e Gerd Gruenert, Gabi Escuela, Peter Dittrich, Thomas Hinze – Uni Jena, Bio Systems Analysis Group 12

Brute Force Approach X F a A b B c C d e Gerd Gruenert, Gabi Escuela, Peter Dittrich, Thomas Hinze – Uni Jena, Bio Systems Analysis Group 13

Random Search using Membrane Receptors Gerd Gruenert, Gabi Escuela, Peter Dittrich, Thomas Hinze – Uni Jena, Bio Systems Analysis Group 14

Random Search using Receptors X F Idea: only consider possible solution a (that produce no overlapping elements) A b B c C d e Gerd Gruenert, Gabi Escuela, Peter Dittrich, Thomas Hinze – Uni Jena, Bio Systems Analysis Group 15

Random Search using Receptors X F Idea: only consider possible solution a (that produce no overlapping elements) A b B c a b c d e C d A x x Algorithm X B x x e (Knuth 2000) C x x x Gerd Gruenert, Gabi Escuela, Peter Dittrich, Thomas Hinze – Uni Jena, Bio Systems Analysis Group 16

Random Search using Receptors X F Idea: only consider possible solution a (that produce no overlapping elements) A b B c C d e A B A B A B C C C Gerd Gruenert, Gabi Escuela, Peter Dittrich, Thomas Hinze – Uni Jena, Bio Systems Analysis Group 17

Random Search using Receptors X F a A b B c C d e C={c,d B={a, A={a, b} ,e} d} A B A B A B C C C Gerd Gruenert, Gabi Escuela, Peter Dittrich, Thomas Hinze – Uni Jena, Bio Systems Analysis Group 18

Random Search using Receptors X F a A b B c C d B a b e a d C c d e C={c,d B={a, A={a, b} ,e} d} A B A B A B C C C Gerd Gruenert, Gabi Escuela, Peter Dittrich, Thomas Hinze – Uni Jena, Bio Systems Analysis Group 19

Random Search using Receptors X F a A b B={a C={c,d B ,b} c ,e} C d B a b e a d C c d e C={c,d B={a, A={a, b} ,e} d} A B A B A B C C C Gerd Gruenert, Gabi Escuela, Peter Dittrich, Thomas Hinze – Uni Jena, Bio Systems Analysis Group 20

Random Search using Receptors X F a c a b d e c d e a b A b B={a C={c,d B ,b} c ,e} C d B a b e a d C c d e C={c,d B={a, A={a, b} ,e} d} A B A B A B C C C Gerd Gruenert, Gabi Escuela, Peter Dittrich, Thomas Hinze – Uni Jena, Bio Systems Analysis Group 21

Random Search using Receptors @model<transition> [lS{6}[rS{6},rS{2}]'C --> [s{6}]'C]'1; def main(){ [lS{7}[rS{7},rS{3}]'C --> [s{7}]'C]'1; /* initial configuration */ [lS{8}[rS{8},rS{4}]'C --> [s{8}]'C]'1; [lS{9}[rS{9},rS{1}]'C --> [s{9}]'C]'1; /* 5 candidate solutions */ [lS{10}[rS{10},rS{2}]'C --> [s{10}]'C]'1; @mu=[[[]'C]'1 [[]'C]'1 [[]'C]'1 [[]'C]'1 [[]'C]'1]'2; /* if there remain open channels, then use them */ /* one ligand for each subset, F X [lS{i}[rS{i},c{m}]'C --> [s{i},c{m}]'C]'1:1<=i<=k,1<=m<n; and a "No" symbol */ A a @ms(1)=lS{1},lS{2},lS{3},lS{4},lS{5}, /* count the elements to evaluate the candidate */ lS{6},lS{7},lS{8},lS{9},lS{10},No; [[s{1}]'C --> s{1}[x{1},x{2},x{3}]'C]'1; B b [[s{2}]'C --> s{2}[x{4},x{5},x{6}]'C]'1; /* one receptor for each subset, C c [[s{3}]'C --> s{3}[x{7},x{8}]'C]'1; and a counter molecule */ [[s{4}]'C --> s{4}[x{9},x{10}]'C]'1; D d @ms(C)=rS{1},rS{2},rS{3},rS{4},rS{5}, [[s{5}]'C --> s{5}[x{1}]'C]'1; rS{6},rS{7},rS{8},rS{9},rS{10},c{0}; E e [[s{6}]'C --> s{6}[x{4}]'C]'1; [[s{7}]'C --> s{7}[x{7}]'C]'1; F f /* local variables */ [[s{8}]'C --> s{8}[x{9}]'C]'1; let n = 10; /* number of elements to cover */ [[s{9}]'C --> s{9}[x{2}]'C]'1; G g let k = 10; /* number of subsets */ [[s{10}]'C --> s{10}[x{5}]'C]'1; H h [x{i},c{m} --> xc{i},c{m+1}]'C:1<=i<=n,0<=m<=n; /* rules */ I i /* if the set is covered then send a /* cooperative rules controlling channels */ J j positive answer to the environment */ [lS{1}[rS{1},rS{5},rS{9}]'C --> [s{1}]'C]'1; [No[c{n}]'C --> Yes[c{n}]'C]'1; [lS{2}[rS{2},rS{6},rS{10}]'C --> [s{2}]'C]'1; [Yes]'1 --> Yes []'1; [lS{3}[rS{3},rS{7}]'C --> [s{3}]'C]'1; [Yes]'2 --> Yes []'2; [lS{4}[rS{4},rS{8}]'C --> [s{4}]'C]'1; } [lS{5}[rS{5},rS{1}]'C --> [s{5}]'C]'1; Gerd Gruenert, Gabi Escuela, Peter Dittrich, Thomas Hinze – Uni Jena, Bio Systems Analysis Group 22

Dynamically Modified Problem Instance Gerd Gruenert, Gabi Escuela, Peter Dittrich, Thomas Hinze – Uni Jena, Bio Systems Analysis Group 23

Dynamically Modified Problem Instance X F Before: Reactions define problem instance. Now: Molecules define problem instance. a A b B c a b d e c d e a b c C d C={c,d ,e} e B a b C c d e C={c,d B={a ,b} ,e} A A B B C C Gerd Gruenert, Gabi Escuela, Peter Dittrich, Thomas Hinze – Uni Jena, Bio Systems Analysis Group 24

Dynamically Modified Problem Instance X F Before: Reactions define problem instance. Now: Molecules define problem instance. a a A b A b B c gen phen c B C d C d e e A B c d e a b C Gerd Gruenert, Gabi Escuela, Peter Dittrich, Thomas Hinze – Uni Jena, Bio Systems Analysis Group 25

Dynamically Modified Problem Instance X F Before: Reactions define problem instance. Now: Molecules define problem instance. a a A b A b B c gen phen c B C d C d e e Gerd Gruenert, Gabi Escuela, Peter Dittrich, Thomas Hinze – Uni Jena, Bio Systems Analysis Group 26

Dynamically Modified Problem Instance X F Before: Reactions define problem instance. Now: Molecules define problem instance. a a A b A b B c gen phen c B C d C d e e + a a b b B c T-c B trans T-C C d T-d a a A B d d e T-e Gerd Gruenert, Gabi Escuela, Peter Dittrich, Thomas Hinze – Uni Jena, Bio Systems Analysis Group 27

Dynamically Modified Problem Instance X F Before: Reactions define problem instance. Now: Molecules define problem instance. a a A b A b B c gen phen c B C d C d T - e C e C c trans T - c d a a b T - d b e B B T - e a a A B d d Gerd Gruenert, Gabi Escuela, Peter Dittrich, Thomas Hinze – Uni Jena, Bio Systems Analysis Group 28

Dynamically Modified Problem Instance X F Before: Reactions define problem instance. Now: Molecules define problem instance. a a A b A b B c gen phen c B T-c C d C d T-d T - e C e T-e C c trans d a a b all or nothing! b e B B a a A B d d Gerd Gruenert, Gabi Escuela, Peter Dittrich, Thomas Hinze – Uni Jena, Bio Systems Analysis Group 29