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

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

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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

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Gerd Gruenert, Gabi Escuela, Peter Dittrich, Thomas Hinze – Uni Jena, Bio Systems Analysis Group 1

Case Study of Molecular Algorithm Design

Gerd Gruenert, Gabi Escuela, Peter Dittrich, Thomas Hinze

Friedrich Schiller University, Jena School of Biology and Pharmacy, Department of Bioinformatics

CMC12, Fontainebleau/Paris, August 2011

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SLIDE 2

Gerd Gruenert, Gabi Escuela, Peter Dittrich, Thomas Hinze – Uni Jena, Bio Systems Analysis Group 2

Word 2007 as Turing Machine?

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Gerd Gruenert, Gabi Escuela, Peter Dittrich, Thomas Hinze – Uni Jena, Bio Systems Analysis Group 3

Word 2007 as Turing Machine?

Morphological Algorithms?

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

Exact Cover Problem

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Gerd Gruenert, Gabi Escuela, Peter Dittrich, Thomas Hinze – Uni Jena, Bio Systems Analysis Group 5

Exact Cover Problem

A B C a b c d e

F X

X = {a,b,c,d,e} F = {A,B,C} A = {a,d} B = {a,b} C = {c,d,e}

Elements: Subsets:

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Gerd Gruenert, Gabi Escuela, Peter Dittrich, Thomas Hinze – Uni Jena, Bio Systems Analysis Group 6

Exact Cover Problem

A B C a b c d e

F X

X = {a,b,c,d,e} F = {A,B,C} A = {a,d} B = {a,b} C = {c,d,e}

Elements: Subsets:

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SLIDE 7

Gerd Gruenert, Gabi Escuela, Peter Dittrich, Thomas Hinze – Uni Jena, Bio Systems Analysis Group 7

Exact Cover Problem

A B C a b c d e

F X

X = {a,b,c,d,e} F = {A,B,C} A = {a,d} B = {a,b} C = {c,d,e}

Elements: Subsets:

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SLIDE 8

Gerd Gruenert, Gabi Escuela, Peter Dittrich, Thomas Hinze – Uni Jena, Bio Systems Analysis Group 8

Exact Cover Problem

X = {a,b,c,d,e} F = {A,B,C} A = {a,d} B = {a,b} C = {c,d,e}

Elements: Subsets: Select Elements such that:

  • All elements from X covered
  • No element from X covered twice

A B C a b c d e

F X

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SLIDE 9

Gerd Gruenert, Gabi Escuela, Peter Dittrich, Thomas Hinze – Uni Jena, Bio Systems Analysis Group 9

Exact Cover Problem

X = {a,b,c,d,e} F = {A,B,C} A = {a,d} B = {a,b} C = {c,d,e}

Elements: Subsets: Select Elements such that:

  • All elements from X covered
  • No element from X covered twice

{B,C} is an exact set cover

  • f X:

✔ X = B ∪ C, and ✔ B ∩ C = ∅

A B C c e

F X

b d a

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SLIDE 10

Gerd Gruenert, Gabi Escuela, Peter Dittrich, Thomas Hinze – Uni Jena, Bio Systems Analysis Group 10

Exact Cover Problem

X = {a,b,c,d,e} F = {A,B,C} A = {a,d} B = {a,b} C = {c,d,e}

Elements: Subsets: Select Elements such that:

  • All elements from X covered
  • No element from X covered twice

a b c d e A x x B x x C x x x {B,C} is an exact set cover

  • f X:

✔ X = B ∪ C, and ✔ B ∩ C = ∅

A B C c e

F X

b d a

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SLIDE 11

Gerd Gruenert, Gabi Escuela, Peter Dittrich, Thomas Hinze – Uni Jena, Bio Systems Analysis Group 11

Brute Force Approach

Rrrrrraar!

A B C c e

F X

b d a

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Gerd Gruenert, Gabi Escuela, Peter Dittrich, Thomas Hinze – Uni Jena, Bio Systems Analysis Group 12

Brute Force Approach

A B C c e

F X

b d a

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Gerd Gruenert, Gabi Escuela, Peter Dittrich, Thomas Hinze – Uni Jena, Bio Systems Analysis Group 13

Brute Force Approach

A B C c e

F X

b d a

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Gerd Gruenert, Gabi Escuela, Peter Dittrich, Thomas Hinze – Uni Jena, Bio Systems Analysis Group 14

Random Search using Membrane Receptors

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Gerd Gruenert, Gabi Escuela, Peter Dittrich, Thomas Hinze – Uni Jena, Bio Systems Analysis Group 15

Random Search using Receptors

A B C c e

F X

b d a

Idea: only consider possible solution (that produce no overlapping elements)

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Gerd Gruenert, Gabi Escuela, Peter Dittrich, Thomas Hinze – Uni Jena, Bio Systems Analysis Group 16

Random Search using Receptors

A B C c e

F X

b d a

Idea: only consider possible solution (that produce no overlapping elements)

a b c d e A x x B x x C x x x

Algorithm X (Knuth 2000)

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Gerd Gruenert, Gabi Escuela, Peter Dittrich, Thomas Hinze – Uni Jena, Bio Systems Analysis Group 17

Random Search using Receptors

C B A C B A C B A

A B C c e

F X

b d a

Idea: only consider possible solution (that produce no overlapping elements)

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Gerd Gruenert, Gabi Escuela, Peter Dittrich, Thomas Hinze – Uni Jena, Bio Systems Analysis Group 18

Random Search using Receptors

C B A

A={a, d} B={a, b}

C B A C B A

C={c,d ,e}

A B C c e

F X

b d a

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Gerd Gruenert, Gabi Escuela, Peter Dittrich, Thomas Hinze – Uni Jena, Bio Systems Analysis Group 19

Random Search using Receptors

a d

C B A

A={a, d} B={a, b}

C B A

a b

C C B A

C={c,d ,e}

c d e

B

A B C c e

F X

b d a

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Gerd Gruenert, Gabi Escuela, Peter Dittrich, Thomas Hinze – Uni Jena, Bio Systems Analysis Group 20

Random Search using Receptors

a d

C B A

A={a, d} B={a, b}

C B A

a b

C

C={c,d ,e}

C B A

C={c,d ,e}

c d e

B

B={a ,b}

A B C c e

F X

b d a

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Gerd Gruenert, Gabi Escuela, Peter Dittrich, Thomas Hinze – Uni Jena, Bio Systems Analysis Group 21

Random Search using Receptors

a d

C B A

A={a, d} B={a, b}

C B A

a b

C

C={c,d ,e}

c a b d e

C B A

C={c,d ,e}

c d e

B

B={a ,b}

c d e a b A B C c e

F X

b d a

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Gerd Gruenert, Gabi Escuela, Peter Dittrich, Thomas Hinze – Uni Jena, Bio Systems Analysis Group 22

Random Search using Receptors

@model<transition> def main(){ /* initial configuration */ /* 5 candidate solutions */ @mu=[[[]'C]'1 [[]'C]'1 [[]'C]'1 [[]'C]'1 [[]'C]'1]'2; /* one ligand for each subset, and a "No" symbol */ @ms(1)=lS{1},lS{2},lS{3},lS{4},lS{5}, lS{6},lS{7},lS{8},lS{9},lS{10},No; /* one receptor for each subset, and a counter molecule */ @ms(C)=rS{1},rS{2},rS{3},rS{4},rS{5}, rS{6},rS{7},rS{8},rS{9},rS{10},c{0}; /* local variables */ let n = 10; /* number of elements to cover */ let k = 10; /* number of subsets */ /* rules */ /* cooperative rules controlling channels */ [lS{1}[rS{1},rS{5},rS{9}]'C --> [s{1}]'C]'1; [lS{2}[rS{2},rS{6},rS{10}]'C --> [s{2}]'C]'1; [lS{3}[rS{3},rS{7}]'C --> [s{3}]'C]'1; [lS{4}[rS{4},rS{8}]'C --> [s{4}]'C]'1; [lS{5}[rS{5},rS{1}]'C --> [s{5}]'C]'1; [lS{6}[rS{6},rS{2}]'C --> [s{6}]'C]'1; [lS{7}[rS{7},rS{3}]'C --> [s{7}]'C]'1; [lS{8}[rS{8},rS{4}]'C --> [s{8}]'C]'1; [lS{9}[rS{9},rS{1}]'C --> [s{9}]'C]'1; [lS{10}[rS{10},rS{2}]'C --> [s{10}]'C]'1; /* if there remain open channels, then use them */ [lS{i}[rS{i},c{m}]'C --> [s{i},c{m}]'C]'1:1<=i<=k,1<=m<n; /* count the elements to evaluate the candidate */ [[s{1}]'C --> s{1}[x{1},x{2},x{3}]'C]'1; [[s{2}]'C --> s{2}[x{4},x{5},x{6}]'C]'1; [[s{3}]'C --> s{3}[x{7},x{8}]'C]'1; [[s{4}]'C --> s{4}[x{9},x{10}]'C]'1; [[s{5}]'C --> s{5}[x{1}]'C]'1; [[s{6}]'C --> s{6}[x{4}]'C]'1; [[s{7}]'C --> s{7}[x{7}]'C]'1; [[s{8}]'C --> s{8}[x{9}]'C]'1; [[s{9}]'C --> s{9}[x{2}]'C]'1; [[s{10}]'C --> s{10}[x{5}]'C]'1; [x{i},c{m} --> xc{i},c{m+1}]'C:1<=i<=n,0<=m<=n; /* if the set is covered then send a positive answer to the environment */ [No[c{n}]'C --> Yes[c{n}]'C]'1; [Yes]'1 --> Yes []'1; [Yes]'2 --> Yes []'2; }

c b d a e C B D A E f g h i j F G H I J

F X

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

Dynamically Modified Problem Instance

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Gerd Gruenert, Gabi Escuela, Peter Dittrich, Thomas Hinze – Uni Jena, Bio Systems Analysis Group 24

Dynamically Modified Problem Instance

Before: Reactions define problem instance. Now: Molecules define problem instance.

A B C c e

F X

b d a

B={a ,b}

C B A

a b

C

C={c,d ,e}

c a b d e

C B A

C={c,d ,e}

c d e

B

c d e a b

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Gerd Gruenert, Gabi Escuela, Peter Dittrich, Thomas Hinze – Uni Jena, Bio Systems Analysis Group 25

Dynamically Modified Problem Instance

phen c

b d a e

gen

C B A

A B C c e

F X

b d a c d e a b

C B A

Before: Reactions define problem instance. Now: Molecules define problem instance.

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Gerd Gruenert, Gabi Escuela, Peter Dittrich, Thomas Hinze – Uni Jena, Bio Systems Analysis Group 26

Dynamically Modified Problem Instance

phen c

b d a e

gen

C B A

A B C c e

F X

b d a

Before: Reactions define problem instance. Now: Molecules define problem instance.

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Gerd Gruenert, Gabi Escuela, Peter Dittrich, Thomas Hinze – Uni Jena, Bio Systems Analysis Group 27

Dynamically Modified Problem Instance

phen c

b d a e

gen

C B A

trans

c d e C T-C T-c T-d T-e

+

a b B a b B a d B A a d

A B C c e

F X

b d a

Before: Reactions define problem instance. Now: Molecules define problem instance.

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Gerd Gruenert, Gabi Escuela, Peter Dittrich, Thomas Hinze – Uni Jena, Bio Systems Analysis Group 28

Dynamically Modified Problem Instance

phen c

b d a e

gen

C B A

a b B a b B a d B A a d

A B C c e

F X

b d a trans

c d e C T

  • C

T

  • c

T

  • d

T

  • e

Before: Reactions define problem instance. Now: Molecules define problem instance.

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Gerd Gruenert, Gabi Escuela, Peter Dittrich, Thomas Hinze – Uni Jena, Bio Systems Analysis Group 29

Dynamically Modified Problem Instance

phen c

b d a e

gen

C B A

a b B a b B a d B A a d

all or nothing! A B C c e

F X

b d a

T-c T-d T-e

trans

c d e C T

  • C

Before: Reactions define problem instance. Now: Molecules define problem instance.

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Gerd Gruenert, Gabi Escuela, Peter Dittrich, Thomas Hinze – Uni Jena, Bio Systems Analysis Group 30

Dynamically Modified Problem Instance

phen c

b d a e

gen

C B A

a b B a b B a d B A a d

A B C c e

F X

b d a trans

c d e C T-c T-d T-e T-C

Before: Reactions define problem instance. Now: Molecules define problem instance.

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Gerd Gruenert, Gabi Escuela, Peter Dittrich, Thomas Hinze – Uni Jena, Bio Systems Analysis Group 31

Dynamically Modified Problem Instance

phen c

b d a e

gen

C B A

a b B a b B a d B A a d

A B C c e

F X

b d a trans

c d e C T-c T-d T-e T-C

Movie: docking1st.mpg

Before: Reactions define problem instance. Now: Molecules define problem instance.

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Gerd Gruenert, Gabi Escuela, Peter Dittrich, Thomas Hinze – Uni Jena, Bio Systems Analysis Group 32

Dynamically Modified Problem Instance

phen c

b d a e

gen

C B A

a b B a b B

A B C c e

F X

b d a trans

c d e C T-c T-d T-e T-C

trans

a d B T-A T-a T-d

Before: Reactions define problem instance. Now: Molecules define problem instance.

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SLIDE 33

Gerd Gruenert, Gabi Escuela, Peter Dittrich, Thomas Hinze – Uni Jena, Bio Systems Analysis Group 33

Dynamically Modified Problem Instance

phen c

b d a e

gen

C B A

a b B a b B

A B C c e

F X

b d a trans

c d e C T-c T-d T-e T-C

trans

a d B T-A T-a T-d

Docking Impossible Before: Reactions define problem instance. Now: Molecules define problem instance.

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Gerd Gruenert, Gabi Escuela, Peter Dittrich, Thomas Hinze – Uni Jena, Bio Systems Analysis Group 34

Assembling Possible Solutions

phen

c b d a e

gen

C B A c b d a e

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Gerd Gruenert, Gabi Escuela, Peter Dittrich, Thomas Hinze – Uni Jena, Bio Systems Analysis Group 35

Assembling Possible Solutions

phen

c b d a e

gen

C B A c b d a e

a d B A a d a b B a b B c d e C C c d e

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SLIDE 36

Gerd Gruenert, Gabi Escuela, Peter Dittrich, Thomas Hinze – Uni Jena, Bio Systems Analysis Group 36

Assembling Possible Solutions

phen

c b d a e

gen

C B A T-A T-a T-d

phen

c b d a e

gen

C B A

phen

c b d a e

gen

C B A T-a T-B T-b

phen

c b d a e

gen

C B A T-C T-c T-d T-e

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SLIDE 37

Gerd Gruenert, Gabi Escuela, Peter Dittrich, Thomas Hinze – Uni Jena, Bio Systems Analysis Group 37

Assembling Possible Solutions

phen

c b d a e

gen

C B A T-A T-a T-d

phen

c b d a e

gen

C B A

phen

c b d a e

gen

C B A T-a T-B T-b

phen

c b d a e

gen

C B A T-C T-c T-d T-e

a b B a b B c d C C c d e

Dead end

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SLIDE 38

Gerd Gruenert, Gabi Escuela, Peter Dittrich, Thomas Hinze – Uni Jena, Bio Systems Analysis Group 38

Assembling Possible Solutions

phen

c b d a e

gen

C B A T-A T-a T-d

phen

c b d a e

gen

C B A

phen

c b d a e

gen

C B A T-a T-B T-b

phen

c b d a e

gen

C B A T-a T-B T-b T-C T-c T-d T-e

phen

c b d a e

gen

C B A T-C T-c T-d T-e

phen

c b d a e

gen

C B A T-a T-B T-b T-C T-c T-d T-e

Dead end

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Gerd Gruenert, Gabi Escuela, Peter Dittrich, Thomas Hinze – Uni Jena, Bio Systems Analysis Group 39

Chemical Description of an Evolutionary Algorithm

Selection Reproduction

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Gerd Gruenert, Gabi Escuela, Peter Dittrich, Thomas Hinze – Uni Jena, Bio Systems Analysis Group 40

We need Selection & Reproduction

phe

c b d a e

gen

C B A T-A T-a T-d

Diversity

phe

c b d a e

gen

C B A T-c T-d T-e T-C

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SLIDE 41

Gerd Gruenert, Gabi Escuela, Peter Dittrich, Thomas Hinze – Uni Jena, Bio Systems Analysis Group 41

phe

c b d a e

gen

C B A T-A T-a T-d

phe

c b d a e

gen

C B A T-c T-d T-e T-C

Copier

Diversity

We need Selection & Reproduction

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SLIDE 42

Gerd Gruenert, Gabi Escuela, Peter Dittrich, Thomas Hinze – Uni Jena, Bio Systems Analysis Group 42

phe

c b d a e

gen

C B A T-A T-a T-d

phe

c b d a e

gen

C B A T-c T-d T-e T-C

Copier

Diversity Selection (stochastic process)

We need Selection & Reproduction

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SLIDE 43

Gerd Gruenert, Gabi Escuela, Peter Dittrich, Thomas Hinze – Uni Jena, Bio Systems Analysis Group 43

phe

c b d a e

gen

C B A T-A T-a T-d

phe

c b d a e

gen

C B A T-c T-d T-e T-C

Copier

Diversity Selection (stochastic process)

We need Selection & Reproduction

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Gerd Gruenert, Gabi Escuela, Peter Dittrich, Thomas Hinze – Uni Jena, Bio Systems Analysis Group 44

phe

c b d a e

gen

C B A T-A T-a T-d

phe

c b d a e

gen

C B A

Copier

Diversity Selection (stochastic process)

We need Selection & Reproduction

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Gerd Gruenert, Gabi Escuela, Peter Dittrich, Thomas Hinze – Uni Jena, Bio Systems Analysis Group 45

trans

c d e C T-C T-c T-d T-e

phe

c b d a e

gen

C B A T-A T-a T-d

Copier trans

a d B T-A T-a T-d

trans

a b B T-a T-b T-B

phe

c b d a e

gen

C B A

Diversity Selection (stochastic process) Reproduction

We need Selection & Reproduction

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SLIDE 46

Gerd Gruenert, Gabi Escuela, Peter Dittrich, Thomas Hinze – Uni Jena, Bio Systems Analysis Group 46

trans

c d e C T-C T-c T-d T-e

phe

c b d a e

gen

C B A T-A T-a T-d

Copier trans

a d B T-A T-a T-d

trans

a b B T-a T-b T-B

phe

c b d a e

gen

C B A

Impossible Possible

We need Selection & Reproduction

Diversity Selection (stochastic process) Reproduction

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SLIDE 47

Gerd Gruenert, Gabi Escuela, Peter Dittrich, Thomas Hinze – Uni Jena, Bio Systems Analysis Group 47

trans

c d e C T-C T-c T-d T-e

phe

c b d a e

gen

C B A T-A T-a T-d

Copier trans

a d B T-A T-a T-d

trans

a b B T-a T-b T-B

phe

c b d a e

gen

C B A

Impossible Possible

We need Selection & Reproduction

T-A T-a T-d

Diversity Selection (stochastic process) Reproduction

slide-48
SLIDE 48

Gerd Gruenert, Gabi Escuela, Peter Dittrich, Thomas Hinze – Uni Jena, Bio Systems Analysis Group 48

trans

c d e C T-C T-c T-d T-e

phe

c b d a e

gen

C B A T-A T-a T-d

Copier trans

a d B T-A T-a T-d

trans

a b B T-a T-b T-B

phe

c b d a e

gen

C B A

Possible

We need Selection & Reproduction

T-A T-a T-d

Diversity Selection (stochastic process) Reproduction (stochastic proc.)

slide-49
SLIDE 49

Gerd Gruenert, Gabi Escuela, Peter Dittrich, Thomas Hinze – Uni Jena, Bio Systems Analysis Group 49

trans

c d e C T-C T-c T-d T-e

phe

c b d a e

gen

C B A T-A T-a T-d

Copier trans

a d B T-A T-a T-d

trans

a b B T-a T-b T-B

phe

c b d a e

gen

C B A

Possible Possible

We need Selection & Reproduction

Diversity Selection (stochastic process) Reproduction Mutation

koff

slide-50
SLIDE 50

Gerd Gruenert, Gabi Escuela, Peter Dittrich, Thomas Hinze – Uni Jena, Bio Systems Analysis Group 50

Random Search using Receptors

T(x~a,t!1).Trans(f!1~a,t!11~a,t!12~b,t!13~c,t,dock~p1).T(x~a,t!11).T(x~b,t!12).T(x~c,t!13) 30 T(x~b,t!1).Trans(f!1~b,t!11~d,t!12~e,t!13~f,t,dock~p1).T(x~d,t!11).T(x~e,t!12).T(x~f,t!13) 30 T(x~c,t!1).Trans(f!1~c,t!11~g,t!12~h,t,t,dock~p1).T(x~g,t!11).T(x~h,t!12) 30 T(x~d,t!1).Trans(f!1~d,t!11~i,t!12~j,t,t,dock~p1).T(x~i,t!11).T(x~j,t!12) 30 T(x~e,t!1).Trans(f!1~e,t!11~a,t,t,t,dock~p1).T(x~a,t!11) 30 T(x~f,t!1).Trans(f!1~f,t!11~d,t,t,t,dock~p1).T(x~d,t!11) 30 T(x~g,t!1).Trans(f!1~g,t!11~g,t,t,t,dock~p1).T(x~g,t!11) 30 T(x~h,t!1).Trans(f!1~h,t!11~i,t,t,t,dock~p1).T(x~i,t!11) 30 T(x~i,t!1).Trans(f!1~i,t!11~b,t,t,t,dock~p1).T(x~b,t!11) 30 T(x~j,t!1).Trans(f!1~j,t!11~e,t,t,t,dock~p1).T(x~e,t!11) 30 1 Sol(test~ok,t~a,eval!+) + T(x~a,t!5).Trans(f!5,dock~p1) -> Sol(test~ok,t~a!1,eval!+).T(x~a!1,t!5).Trans(f!5,dock~p1) kFastBind 1 Sol(test~ok,t~b,eval!+) + T(x~b,t!5).Trans(f!5,dock~p1) -> Sol(test~ok,t~b!1,eval!+).T(x~b!1,t!5).Trans(f!5,dock~p1) kFastBind 1 Sol(test~ok,t~c,eval!+) + T(x~c,t!5).Trans(f!5,dock~p1) -> Sol(test~ok,t~c!1,eval!+).T(x~c!1,t!5).Trans(f!5,dock~p1) kFastBind 1 Sol(test~ok,t~d,eval!+) + T(x~d,t!5).Trans(f!5,dock~p1) -> Sol(test~ok,t~d!1,eval!+).T(x~d!1,t!5).Trans(f!5,dock~p1) kFastBind 1 Sol(test~ok,t~e,eval!+) + T(x~e,t!5).Trans(f!5,dock~p1) -> Sol(test~ok,t~e!1,eval!+).T(x~e!1,t!5).Trans(f!5,dock~p1) kFastBind 1 Sol(test~ok,t~f,eval!+) + T(x~f,t!5).Trans(f!5,dock~p1) -> Sol(test~ok,t~f!1,eval!+).T(x~f!1,t!5).Trans(f!5,dock~p1) kFastBind 1 Sol(test~ok,t~g,eval!+) + T(x~g,t!5).Trans(f!5,dock~p1) -> Sol(test~ok,t~g!1,eval!+).T(x~g!1,t!5).Trans(f!5,dock~p1) kFastBind 1 Sol(test~ok,t~h,eval!+) + T(x~h,t!5).Trans(f!5,dock~p1) -> Sol(test~ok,t~h!1,eval!+).T(x~h!1,t!5).Trans(f!5,dock~p1) kFastBind 1 Sol(test~ok,t~i,eval!+) + T(x~i,t!5).Trans(f!5,dock~p1) -> Sol(test~ok,t~i!1,eval!+).T(x~i!1,t!5).Trans(f!5,dock~p1) kFastBind 1 Sol(test~ok,t~j,eval!+) + T(x~j,t!5).Trans(f!5,dock~p1) -> Sol(test~ok,t~j!1,eval!+).T(x~j!1,t!5).Trans(f!5,dock~p1) kFastBind # dissociate, if dock~bad 1 Sol(t!1).T(x!1,t!5).Trans(f!5,dock~bad) -> Sol(t) + T(x,t!5).Trans(f!5,dock~bad) kTDissociate # bind evaluation components: (if not bound to copyTo) 2 Sol(test~ok,eval!2).Eval(t~a,sol!2) + T(x~a,t!5).Trans(t!5,dock~p1) -> Sol(test~ok,eval!2).Eval(t~a!1,sol!2).T(x~a!1,t!5).Trans(t!5,dock~p1) kFastBind 2 Sol(test~ok,eval!2).Eval(t~b,sol!2) + T(x~b,t!5).Trans(t!5,dock~p1) -> Sol(test~ok,eval!2).Eval(t~b!1,sol!2).T(x~b!1,t!5).Trans(t!5,dock~p1) kFastBind 2 Sol(test~ok,eval!2).Eval(t~c,sol!2) + T(x~c,t!5).Trans(t!5,dock~p1) -> Sol(test~ok,eval!2).Eval(t~c!1,sol!2).T(x~c!1,t!5).Trans(t!5,dock~p1) kFastBind 2 Sol(test~ok,eval!2).Eval(t~d,sol!2) + T(x~d,t!5).Trans(t!5,dock~p1) -> Sol(test~ok,eval!2).Eval(t~d!1,sol!2).T(x~d!1,t!5).Trans(t!5,dock~p1) kFastBind 2 Sol(test~ok,eval!2).Eval(t~e,sol!2) + T(x~e,t!5).Trans(t!5,dock~p1) -> Sol(test~ok,eval!2).Eval(t~e!1,sol!2).T(x~e!1,t!5).Trans(t!5,dock~p1) kFastBind 2 Sol(test~ok,eval!2).Eval(t~f,sol!2) + T(x~f,t!5).Trans(t!5,dock~p1) -> Sol(test~ok,eval!2).Eval(t~f!1,sol!2).T(x~f!1,t!5).Trans(t!5,dock~p1) kFastBind 2 Sol(test~ok,eval!2).Eval(t~g,sol!2) + T(x~g,t!5).Trans(t!5,dock~p1) -> Sol(test~ok,eval!2).Eval(t~g!1,sol!2).T(x~g!1,t!5).Trans(t!5,dock~p1) kFastBind 2 Sol(test~ok,eval!2).Eval(t~h,sol!2) + T(x~h,t!5).Trans(t!5,dock~p1) -> Sol(test~ok,eval!2).Eval(t~h!1,sol!2).T(x~h!1,t!5).Trans(t!5,dock~p1) kFastBind 2 Sol(test~ok,eval!2).Eval(t~i,sol!2) + T(x~i,t!5).Trans(t!5,dock~p1) -> Sol(test~ok,eval!2).Eval(t~i!1,sol!2).T(x~i!1,t!5).Trans(t!5,dock~p1) kFastBind 2 Sol(test~ok,eval!2).Eval(t~j,sol!2) + T(x~j,t!5).Trans(t!5,dock~p1) -> Sol(test~ok,eval!2).Eval(t~j!1,sol!2).T(x~j!1,t!5).Trans(t!5,dock~p1) kFastBind # dissociate if dock~bad 2 Eval(t!1).T(x!1,t!5).Trans(t!5,dock~bad) -> Eval(t) + T(x,t!5).Trans(t!5,dock~bad) kTDissociate

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SLIDE 51

Gerd Gruenert, Gabi Escuela, Peter Dittrich, Thomas Hinze – Uni Jena, Bio Systems Analysis Group 51

Random Search using Receptors

T(x~a,t!1).Trans(f!1~a,t!11~a,t!12~b,t!13~c,t,dock~p1).T(x~a,t!11).T(x~b,t!12).T(x~c,t!13) 30 T(x~b,t!1).Trans(f!1~b,t!11~d,t!12~e,t!13~f,t,dock~p1).T(x~d,t!11).T(x~e,t!12).T(x~f,t!13) 30 T(x~c,t!1).Trans(f!1~c,t!11~g,t!12~h,t,t,dock~p1).T(x~g,t!11).T(x~h,t!12) 30 T(x~d,t!1).Trans(f!1~d,t!11~i,t!12~j,t,t,dock~p1).T(x~i,t!11).T(x~j,t!12) 30 T(x~e,t!1).Trans(f!1~e,t!11~a,t,t,t,dock~p1).T(x~a,t!11) 30 T(x~f,t!1).Trans(f!1~f,t!11~d,t,t,t,dock~p1).T(x~d,t!11) 30 T(x~g,t!1).Trans(f!1~g,t!11~g,t,t,t,dock~p1).T(x~g,t!11) 30 T(x~h,t!1).Trans(f!1~h,t!11~i,t,t,t,dock~p1).T(x~i,t!11) 30 T(x~i,t!1).Trans(f!1~i,t!11~b,t,t,t,dock~p1).T(x~b,t!11) 30 T(x~j,t!1).Trans(f!1~j,t!11~e,t,t,t,dock~p1).T(x~e,t!11) 30 1 Sol(test~ok,t~a,eval!+) + T(x~a,t!5).Trans(f!5,dock~p1) -> Sol(test~ok,t~a!1,eval!+).T(x~a!1,t!5).Trans(f!5,dock~p1) kFastBind 1 Sol(test~ok,t~b,eval!+) + T(x~b,t!5).Trans(f!5,dock~p1) -> Sol(test~ok,t~b!1,eval!+).T(x~b!1,t!5).Trans(f!5,dock~p1) kFastBind 1 Sol(test~ok,t~c,eval!+) + T(x~c,t!5).Trans(f!5,dock~p1) -> Sol(test~ok,t~c!1,eval!+).T(x~c!1,t!5).Trans(f!5,dock~p1) kFastBind 1 Sol(test~ok,t~d,eval!+) + T(x~d,t!5).Trans(f!5,dock~p1) -> Sol(test~ok,t~d!1,eval!+).T(x~d!1,t!5).Trans(f!5,dock~p1) kFastBind 1 Sol(test~ok,t~e,eval!+) + T(x~e,t!5).Trans(f!5,dock~p1) -> Sol(test~ok,t~e!1,eval!+).T(x~e!1,t!5).Trans(f!5,dock~p1) kFastBind 1 Sol(test~ok,t~f,eval!+) + T(x~f,t!5).Trans(f!5,dock~p1) -> Sol(test~ok,t~f!1,eval!+).T(x~f!1,t!5).Trans(f!5,dock~p1) kFastBind 1 Sol(test~ok,t~g,eval!+) + T(x~g,t!5).Trans(f!5,dock~p1) -> Sol(test~ok,t~g!1,eval!+).T(x~g!1,t!5).Trans(f!5,dock~p1) kFastBind 1 Sol(test~ok,t~h,eval!+) + T(x~h,t!5).Trans(f!5,dock~p1) -> Sol(test~ok,t~h!1,eval!+).T(x~h!1,t!5).Trans(f!5,dock~p1) kFastBind 1 Sol(test~ok,t~i,eval!+) + T(x~i,t!5).Trans(f!5,dock~p1) -> Sol(test~ok,t~i!1,eval!+).T(x~i!1,t!5).Trans(f!5,dock~p1) kFastBind 1 Sol(test~ok,t~j,eval!+) + T(x~j,t!5).Trans(f!5,dock~p1) -> Sol(test~ok,t~j!1,eval!+).T(x~j!1,t!5).Trans(f!5,dock~p1) kFastBind # dissociate, if dock~bad 1 Sol(t!1).T(x!1,t!5).Trans(f!5,dock~bad) -> Sol(t) + T(x,t!5).Trans(f!5,dock~bad) kTDissociate # bind evaluation components: (if not bound to copyTo) 2 Sol(test~ok,eval!2).Eval(t~a,sol!2) + T(x~a,t!5).Trans(t!5,dock~p1) -> Sol(test~ok,eval!2).Eval(t~a!1,sol!2).T(x~a!1,t!5).Trans(t!5,dock~p1) kFastBind 2 Sol(test~ok,eval!2).Eval(t~b,sol!2) + T(x~b,t!5).Trans(t!5,dock~p1) -> Sol(test~ok,eval!2).Eval(t~b!1,sol!2).T(x~b!1,t!5).Trans(t!5,dock~p1) kFastBind 2 Sol(test~ok,eval!2).Eval(t~c,sol!2) + T(x~c,t!5).Trans(t!5,dock~p1) -> Sol(test~ok,eval!2).Eval(t~c!1,sol!2).T(x~c!1,t!5).Trans(t!5,dock~p1) kFastBind 2 Sol(test~ok,eval!2).Eval(t~d,sol!2) + T(x~d,t!5).Trans(t!5,dock~p1) -> Sol(test~ok,eval!2).Eval(t~d!1,sol!2).T(x~d!1,t!5).Trans(t!5,dock~p1) kFastBind 2 Sol(test~ok,eval!2).Eval(t~e,sol!2) + T(x~e,t!5).Trans(t!5,dock~p1) -> Sol(test~ok,eval!2).Eval(t~e!1,sol!2).T(x~e!1,t!5).Trans(t!5,dock~p1) kFastBind 2 Sol(test~ok,eval!2).Eval(t~f,sol!2) + T(x~f,t!5).Trans(t!5,dock~p1) -> Sol(test~ok,eval!2).Eval(t~f!1,sol!2).T(x~f!1,t!5).Trans(t!5,dock~p1) kFastBind 2 Sol(test~ok,eval!2).Eval(t~g,sol!2) + T(x~g,t!5).Trans(t!5,dock~p1) -> Sol(test~ok,eval!2).Eval(t~g!1,sol!2).T(x~g!1,t!5).Trans(t!5,dock~p1) kFastBind 2 Sol(test~ok,eval!2).Eval(t~h,sol!2) + T(x~h,t!5).Trans(t!5,dock~p1) -> Sol(test~ok,eval!2).Eval(t~h!1,sol!2).T(x~h!1,t!5).Trans(t!5,dock~p1) kFastBind 2 Sol(test~ok,eval!2).Eval(t~i,sol!2) + T(x~i,t!5).Trans(t!5,dock~p1) -> Sol(test~ok,eval!2).Eval(t~i!1,sol!2).T(x~i!1,t!5).Trans(t!5,dock~p1) kFastBind 2 Sol(test~ok,eval!2).Eval(t~j,sol!2) + T(x~j,t!5).Trans(t!5,dock~p1) -> Sol(test~ok,eval!2).Eval(t~j!1,sol!2).T(x~j!1,t!5).Trans(t!5,dock~p1) kFastBind # dissociate if dock~bad 2 Eval(t!1).T(x!1,t!5).Trans(t!5,dock~bad) -> Eval(t) + T(x,t!5).Trans(t!5,dock~bad) kTDissociate

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SLIDE 52

Gerd Gruenert, Gabi Escuela, Peter Dittrich, Thomas Hinze – Uni Jena, Bio Systems Analysis Group 52

Random Search using Receptors

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Extremely high mutation rate Each curve is averaged Over 100 runs. Medium mutation rate Low mutation rate Zero mutation rate

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SLIDE 53

Gerd Gruenert, Gabi Escuela, Peter Dittrich, Thomas Hinze – Uni Jena, Bio Systems Analysis Group 53

Random Search using Receptors

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Extremely high mutation rate Each curve is averaged Over 100 runs. Medium mutation rate Low mutation rate Zero mutation rate 140 dissociations 110 dissociations 12 dissociations 0 dissociations

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SLIDE 54

Gerd Gruenert, Gabi Escuela, Peter Dittrich, Thomas Hinze – Uni Jena, Bio Systems Analysis Group 54

Random Search using Receptors

c b d a e C B D A E f g h i j F G H I J

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Extremely high mutation rate Medium mutation rate Low mutation rate Zero mutation rate 140 dissociations 110 dissociations 12 dissociations 0 dissociations

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SLIDE 55

Gerd Gruenert, Gabi Escuela, Peter Dittrich, Thomas Hinze – Uni Jena, Bio Systems Analysis Group 55

Summary / Conclusions Morphological Algorithms?

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SLIDE 56

Gerd Gruenert, Gabi Escuela, Peter Dittrich, Thomas Hinze – Uni Jena, Bio Systems Analysis Group 56

Conclusion

Is there a better substrate for evolutionary algorithms than molecules themselves?

  • large population sizes
  • space
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SLIDE 57

Gerd Gruenert, Gabi Escuela, Peter Dittrich, Thomas Hinze – Uni Jena, Bio Systems Analysis Group 57

Conclusion

Is there a better substrate for evolutionary algorithms than molecules themselves?

  • large population sizes
  • space

Object Oriented Programming for Molecular Computing?

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SLIDE 58

Gerd Gruenert, Gabi Escuela, Peter Dittrich, Thomas Hinze – Uni Jena, Bio Systems Analysis Group 58

Conclusion

Is there a better substrate for evolutionary algorithms than molecules themselves?

  • large population sizes
  • space

Object Oriented Programming for Molecular Computing? Using local rules only. Async, no global stages.

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SLIDE 59

Gerd Gruenert, Gabi Escuela, Peter Dittrich, Thomas Hinze – Uni Jena, Bio Systems Analysis Group 59

Conclusion

Is there a better substrate for evolutionary algorithms than molecules themselves?

  • large population sizes
  • space

Object Oriented Programming for Molecular Computing? Using local rules only. Async, no global stages. Heuristics instead of enumeration.

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SLIDE 60

Gerd Gruenert, Gabi Escuela, Peter Dittrich, Thomas Hinze – Uni Jena, Bio Systems Analysis Group 60

Conclusion

Is there a better substrate for evolutionary algorithms than molecules themselves?

  • large population sizes
  • space

Object Oriented Programming for Molecular Computing? Using local rules only. Async, no global stages. Heuristics instead of enumeration. Continuous optimization with changing objective functions... (Problem instance defined by molec.)

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SLIDE 61

Gerd Gruenert, Gabi Escuela, Peter Dittrich, Thomas Hinze – Uni Jena, Bio Systems Analysis Group 61

Thank you for listening

The “Extended” Bio Systems Analysis Group

Images from: Wikipedia users Yikrazuul, Valeryns