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Motivation Operations on DNA Solution to Knapsack Problem Perspectives
In-vitro Molecular ComputingBased on DNA Strands
An unconventional computing concept inspired by nature
PD Dr. Thomas Hinze
Brandenburg University of Technology Cottbus – SenftenbergInstitute of Computer Science and Information and Media Technology
In-vitro Molecular Computing Based on DNA Strands Thomas Hinze
Motivation Operations on DNA Solution to Knapsack Problem Perspectives
DNA as an Excellent Data Storage Medium
high storagedensity up to
1 bit / nm3
L.M. Adleman. Molecular Computation of Solutions to Combinatorial Problems. Science 266:1021-1024, 1994
In-vitro Molecular Computing Based on DNA Strands Thomas Hinze
Motivation Operations on DNA Solution to Knapsack Problem Perspectives
DNA as an Excellent Data Storage Medium
A C GT
high storagedensity up to
1
base pair in strand ofdeoxyribonucleic acid (DNA)
00 01 10 11
2 bit per nucleotide or per
bit / nm3
L.M. Adleman. Molecular Computation of Solutions to Combinatorial Problems. Science 266:1021-1024, 1994
In-vitro Molecular Computing Based on DNA Strands Thomas Hinze
Motivation Operations on DNA Solution to Knapsack Problem Perspectives
DNA as an Excellent Data Storage Medium
A
A
A
A
C
A
C
C
T
G
T
T
T
G
T
G
A C GT
high storagedensity up to
1
base pair in strand ofdeoxyribonucleic acid (DNA)
00 01 10 11
2 bit per nucleotide or per
5’
5’ 3’
3’
2 nm3 / base pair
bit / nm3
L.M. Adleman. Molecular Computation of Solutions to Combinatorial Problems. Science 266:1021-1024, 1994
In-vitro Molecular Computing Based on DNA Strands Thomas Hinze
Motivation Operations on DNA Solution to Knapsack Problem Perspectives
DNA as an Excellent Data Storage Medium
A
A
A
A
C
A
C
C
T
G
T
T
T
G
T
G
A C GT
high storagedensity up to
1
base pair in strand ofdeoxyribonucleic acid (DNA)
00 01 10 11
2 bit per nucleotide or per
electronicflash memory card
30.001 bit / nm
corresponds to
128 Gbit / 146 qmm
5’
5’ 3’
3’
2 nm3 / base pair
bit / nm3
L.M. Adleman. Molecular Computation of Solutions to Combinatorial Problems. Science 266:1021-1024, 1994
In-vitro Molecular Computing Based on DNA Strands Thomas Hinze
Motivation Operations on DNA Solution to Knapsack Problem Perspectives
DNA as an Excellent Data Storage Medium
high storagepersistence up toseveral thousand years
W. Miller et al. Sequencing the nuclear genome of the extinct woolly mammoth. Nature 456:387-391, 2008
In-vitro Molecular Computing Based on DNA Strands Thomas Hinze
Motivation Operations on DNA Solution to Knapsack Problem Perspectives
DNA as an Excellent Data Storage Medium
under optimalenvironmental conditions
high storagepersistence up toseveral thousand years
W. Miller et al. Sequencing the nuclear genome of the extinct woolly mammoth. Nature 456:387-391, 2008
In-vitro Molecular Computing Based on DNA Strands Thomas Hinze
Motivation Operations on DNA Solution to Knapsack Problem Perspectives
DNA as an Excellent Data Storage Medium
www.zmescience.com
from >20,000 years old mammothapprox. 80% of genome reconstructed
under optimalenvironmental conditions
high storagepersistence up toseveral thousand years
W. Miller et al. Sequencing the nuclear genome of the extinct woolly mammoth. Nature 456:387-391, 2008
In-vitro Molecular Computing Based on DNA Strands Thomas Hinze
Motivation Operations on DNA Solution to Knapsack Problem Perspectives
DNA as an Excellent Data Storage Medium
www.zmescience.com
from >20,000 years old mammothapprox. 80% of genome reconstructed
high storagepersistence up toseveral thousand years
floppy disk: hard disk: DVD (expected):5 ... 10 years 10 ... 15 years 30 ... 50 years
under optimalenvironmental conditions
W. Miller et al. Sequencing the nuclear genome of the extinct woolly mammoth. Nature 456:387-391, 2008
In-vitro Molecular Computing Based on DNA Strands Thomas Hinze
Motivation Operations on DNA Solution to Knapsack Problem Perspectives
DNA as an Excellent Data Storage Medium
highly efficientchemical processingby low energy consumption
L. Kari. Arrival of biological mathematics. The Mathematical Intelligencer 19(2):9-22, 1997
In-vitro Molecular Computing Based on DNA Strands Thomas Hinze
Motivation Operations on DNA Solution to Knapsack Problem Perspectives
DNA as an Excellent Data Storage Medium
: hydrogen bond: covalent bond
Guanine
Cytosine
3’
3’
5’
Thymine
5’
Adenine
A
T
G
C
A
T
G
C
A G
T C
(break or form
internucleotide
chemical bond)
per Joule
elementary operations
up to 1018
highly efficientchemical processingby low energy consumption
O
N
C
C
C
N
NN
CH
O
C
H
H
N
H
N
C
C
N
NN
CH
CH
HH
N
C
O
N
H
C
N
C
C
C
H
N
CH3
H
N
C
O
N
CC
C HO
CH2
CH
CH CH2
CH
2’3’
1’4’
5’
O
CH2
CH
CH CH2
CH
2’3’
1’4’
5’
OH
O
P OO
O
OH
OH
O
CH2
CHCH
CH2
CH
4’
5’
1’
3’2’
CH2
CHCH
CH2
CH
4’
5’
1’
3’2’
OH
P OOO
O
O
L. Kari. Arrival of biological mathematics. The Mathematical Intelligencer 19(2):9-22, 1997
In-vitro Molecular Computing Based on DNA Strands Thomas Hinze
Motivation Operations on DNA Solution to Knapsack Problem Perspectives
DNA as an Excellent Data Storage Medium
: hydrogen bond: covalent bond
Guanine
Cytosine
3’
3’
5’
Thymine
5’
Adenine
A
T
G
C
A
T
G
C
A G
T C
(break or form
internucleotide
chemical bond)
per Joule
elementary operations
up to 1018
10160 1
bit set
or reset
electronically
highly efficientchemical processingby low energy consumption
O
N
C
C
C
N
NN
CH
O
C
H
H
N
H
N
C
C
N
NN
CH
CH
HH
N
C
O
N
H
C
N
C
C
C
H
N
CH3
H
N
C
O
N
CC
C HO
CH2
CH
CH CH2
CH
2’3’
1’4’
5’
O
CH2
CH
CH CH2
CH
2’3’
1’4’
5’
OH
O
P OO
O
OH
OH
O
CH2
CHCH
CH2
CH
4’
5’
1’
3’2’
CH2
CHCH
CH2
CH
4’
5’
1’
3’2’
OH
P OOO
O
O
L. Kari. Arrival of biological mathematics. The Mathematical Intelligencer 19(2):9-22, 1997
In-vitro Molecular Computing Based on DNA Strands Thomas Hinze
Motivation Operations on DNA Solution to Knapsack Problem Perspectives
DNA as an Excellent Data Storage Medium
massivedataparallelism
L.M. Adleman. Molecular Computation of Solutions to Combinatorial Problems. Science 266:1021-1024, 1994
In-vitro Molecular Computing Based on DNA Strands Thomas Hinze
Motivation Operations on DNA Solution to Knapsack Problem Perspectives
DNA as an Excellent Data Storage Medium
up to 1015
molecules
DNA and other
massivedataparallelism
DNA strands
per test tube (2ml)
simultaneous
and autonomous
molecular interactions
without central control
L.M. Adleman. Molecular Computation of Solutions to Combinatorial Problems. Science 266:1021-1024, 1994
In-vitro Molecular Computing Based on DNA Strands Thomas Hinze
Motivation Operations on DNA Solution to Knapsack Problem Perspectives
on DNA
Operations
2.
In-vitro Molecular Computing Based on DNA Strands Thomas Hinze
Motivation Operations on DNA Solution to Knapsack Problem Perspectives
Operations on DNA (Selection)Gaining DNA strands
• Synthesis (oligos) 5’−ACGGAAC−3’ A C G G A A C
• Isolation (like plasmids or genomic DNA from organisms)
Handling DNA solutions
• Union (merge)
• Split (aliquot)
Forming and breaking hydrogen bonds
• Annealing (hybridisation)T T G C C T T
A C G G A A C
T
A
T
C
G
G
C
G
C
A
T
A
T
C
• Melting (denaturation) T
A
T
C
G
G
C
G
C
A
T
A
T
C
T T G C C T T
A C G G A A C
In-vitro Molecular Computing Based on DNA Strands Thomas Hinze
Motivation Operations on DNA Solution to Knapsack Problem Perspectives
Operations on DNA (Selection)Gaining DNA strands
• Synthesis (oligos) 5’−ACGGAAC−3’ A C G G A A C
• Isolation (like plasmids or genomic DNA from organisms)
Handling DNA solutions
• Union (merge)
• Split (aliquot)
Forming and breaking hydrogen bonds
• Annealing (hybridisation)T T G C C T T
A C G G A A C
T
A
T
C
G
G
C
G
C
A
T
A
T
C
• Melting (denaturation) T
A
T
C
G
G
C
G
C
A
T
A
T
C
T T G C C T T
A C G G A A C
In-vitro Molecular Computing Based on DNA Strands Thomas Hinze
Motivation Operations on DNA Solution to Knapsack Problem Perspectives
Operations on DNA (Selection)Gaining DNA strands
• Synthesis (oligos) 5’−ACGGAAC−3’ A C G G A A C
• Isolation (like plasmids or genomic DNA from organisms)
Handling DNA solutions
• Union (merge)
• Split (aliquot)
Forming and breaking hydrogen bonds
• Annealing (hybridisation)T T G C C T T
A C G G A A C
T
A
T
C
G
G
C
G
C
A
T
A
T
C
• Melting (denaturation) T
A
T
C
G
G
C
G
C
A
T
A
T
C
T T G C C T T
A C G G A A C
In-vitro Molecular Computing Based on DNA Strands Thomas Hinze
Motivation Operations on DNA Solution to Knapsack Problem Perspectives
Operations on DNA (Selection)Enzymatically catalysed reactions
• Ligation (concatenation)................T
A
C
G
G
C A P
T A
T
T
A
P T
A
C
G
G
C
T
A
A
T
T
A
• Digestion (cleavage).....................A
T
G
C
C
G
G
C
C
G
A
THinP1 I
A
T
G
C G C P
C G C
G
A
T
PG
C
C
G
G
C
C
G
5’
3’
3’
5’
• Labelling (strand end modification)A
T
G
C
C
G
G
C
C
G
A
T
A
T
G
C
C
G
G
C
C
G
A
T
P
P+ 5’−Phosphat
• Polymerisation (completion)..........A G C
G
G
C
C A A
T
G
C
C
G
G
C
• PCR (polymerase chain reaction)... ........ duplicate strands
Separation and analysis of DNA strands
• Affinity purification (sep. by biotin)..A C
G
C
G
T
A
A
T
G
C TC
B T
A
A
T
T
A + 5’−Biotin TC
B T
A
A
T
T
A
• Gel electrophoresis (sep. by length) sort and detect strands
• Sequencing (readout).......................A C G G A A C 5’−ACGGAAC−3’
In-vitro Molecular Computing Based on DNA Strands Thomas Hinze
Motivation Operations on DNA Solution to Knapsack Problem Perspectives
Operations on DNA (Selection)Enzymatically catalysed reactions
• Ligation (concatenation)................T
A
C
G
G
C A P
T A
T
T
A
P T
A
C
G
G
C
T
A
A
T
T
A
• Digestion (cleavage).....................A
T
G
C
C
G
G
C
C
G
A
THinP1 I
A
T
G
C G C P
C G C
G
A
T
PG
C
C
G
G
C
C
G
5’
3’
3’
5’
• Labelling (strand end modification)A
T
G
C
C
G
G
C
C
G
A
T
A
T
G
C
C
G
G
C
C
G
A
T
P
P+ 5’−Phosphat
• Polymerisation (completion)..........A G C
G
G
C
C A A
T
G
C
C
G
G
C
• PCR (polymerase chain reaction)... ........ duplicate strands
Separation and analysis of DNA strands
• Affinity purification (sep. by biotin)..A C
G
C
G
T
A
A
T
G
C TC
B T
A
A
T
T
A + 5’−Biotin TC
B T
A
A
T
T
A
• Gel electrophoresis (sep. by length) sort and detect strands
• Sequencing (readout).......................A C G G A A C 5’−ACGGAAC−3’
In-vitro Molecular Computing Based on DNA Strands Thomas Hinze
Motivation Operations on DNA Solution to Knapsack Problem Perspectives
NP−hard Knapsack Problem
Algorithm for Solution to the
3.
In-vitro Molecular Computing Based on DNA Strands Thomas Hinze
Motivation Operations on DNA Solution to Knapsack Problem Perspectives
Knapsack ProblemNP-hard decision problem, exponential need of resources
DefinitionGiven n natural numbers a1, ...,an and reference number b ∈ NIs there a subset I ⊆ {1, ...,n} with
∑i∈I
ai = b ?
Explanationa1, ...,an: weights of objects 1, ...,n.Is there a possibility to pack a selection of these objects intothe knapsack which exactly meets the reference weight b?
Example
.
9 95
7 7
2
2
a = 7a = 2b = 9
1
2
3
a = 5
?object 2
object 1
object 3 "yes"solution
In-vitro Molecular Computing Based on DNA Strands Thomas Hinze
Motivation Operations on DNA Solution to Knapsack Problem Perspectives
Idea of Wetware Solution to Knapsack Problem
Brute force approach• Encode a1, . . . ,an into DNA double strands by length (c ·ai )• Generate all solution candidates by a controlled
split-and-combine strategy• Separate final DNA pool by length• Detect DNA at Starter length + c · b and answer yes
by lengthseparation
10
20
30
5
15
25
35
a1
Starter
Starter
a1Starter Starter
Starter
Starter
Starter
a1
a1
a2
a2
a2
Starter
Starter
Starter
Starter
Starter
Starter
Starter
Starter
a1
a2
a1
a2
a1 a2
a1 a2
DNA operationsDNA operations DNA operations
a3
a3
a3
a3
a3
M. Sturm, T. Hinze. Verfahren zur Ausführung von mathematischen Operationen mittels eines DNA-Computers undDNA-Computer hierzu. Deutsches Patent DE 101 59 886 B4, IPC G06N 3/00, erteilt 2010
In-vitro Molecular Computing Based on DNA Strands Thomas Hinze
Motivation Operations on DNA Solution to Knapsack Problem Perspectives
Split-and-combine Strategydoubles number of combinations by addition of one object
Union
Ligation
Split
Union
DNA pool composed of combinations from k objectsstart with k = 0 (starters only)
DNA pool composed of combinations from k+1 objects
Labelling 5’+Padd object a_(k+1)
Starter
Starter
Starter
Starter
a1
a1
a2
a2
a2
Starter
a1Starter
a2
a2
a1Starter
Starter
In-vitro Molecular Computing Based on DNA Strands Thomas Hinze
Motivation Operations on DNA Solution to Knapsack Problem Perspectives
Simple Implementation of a Problem Instance• n = 3 objects taken from plasmid (pQE30 cleaved with PvuII)
• a1 = 719, a2 = 393, a3 = 270, b = 1112, c = 1
• Exponential need of resources moved from time to space
• Final sequencing of DNA band corresponding to b reveals “yes”
• Limited scalability of the algorithm due to side effects andamount of DNA
100
1000
1200
1
719 bp
393 bp
270 bp
750 bp
500 bp
250 bp
150 bp
bp
270270
393393
663393 270
719719
719 270
719 393
719 393 270
989
1112
1382
bp2 1 2 3
In-vitro Molecular Computing Based on DNA Strands Thomas Hinze
Motivation Operations on DNA Solution to Knapsack Problem Perspectives
Side Effects and Perturbationsprevent DNA operations from running in an ideal manner
• Loss of DNA• Incomplete reactions• Non-specificities• Malformed DNA (artefacts)• DNA damage• Contaminations or impurities of DNA solutions• . . . (many others)
Coping with side effects is a hard challenge to overcome inpractical in-vitro DNA computation. Assuming an error rate of5% per operation and having a sequence of 10 operations, theoverall success rate is merely 0.9510 · 100 ≈ 60%.
In-vitro Molecular Computing Based on DNA Strands Thomas Hinze
Motivation Operations on DNA Solution to Knapsack Problem Perspectives
Trends, and Perspectives
Further Applications,
4.
In-vitro Molecular Computing Based on DNA Strands Thomas Hinze
Motivation Operations on DNA Solution to Knapsack Problem Perspectives
Milestones of DNA-based Computing• Pioneering era after Adleman’s experiment
• Refinement and improvement of techniques and encodingschemes complemented by much theoretical work
• Addressable DNA-based memory able to store data from files
• Computing by DNA self-assembly promising clue towardsfreely programmable nanomachines
Adleman’s
DNA−based solution to
Hamiltonian path problem
(n = 7 nodes)
www.usc.edu
1994
DNA−based solution to
satisfiability problem
by brute force approach
(n = 20 variables)
www.sciencemag.org
2002
In-vitro Molecular Computing Based on DNA Strands Thomas Hinze
Motivation Operations on DNA Solution to Knapsack Problem Perspectives
Milestones of DNA-based Computing• Pioneering era after Adleman’s experiment
• Refinement and improvement of techniques and encodingschemes complemented by much theoretical work
• Addressable DNA-based memory able to store data from files
• Computing by DNA self-assembly promising clue towardsfreely programmable nanomachines
Adleman’s
DNA−based solution to
Hamiltonian path problem
(n = 7 nodes)
www.usc.edu
1994
DNA−based solution to
satisfiability problem
by brute force approach
(n = 20 variables)
www.sciencemag.org
2002
DNA chips for
massive parallel computing
by string matching
approx. 40,000 spots
2010
www.newscientist.com
In-vitro Molecular Computing Based on DNA Strands Thomas Hinze
Motivation Operations on DNA Solution to Knapsack Problem Perspectives
Milestones of DNA-based Computing• Pioneering era after Adleman’s experiment
• Refinement and improvement of techniques and encodingschemes complemented by much theoretical work
• Addressable DNA-based memory able to store data from files
• Computing by DNA self-assembly promising clue towardsfreely programmable nanomachines
Adleman’s
DNA−based solution to
Hamiltonian path problem
(n = 7 nodes)
www.usc.edu
1994
DNA−based solution to
satisfiability problem
by brute force approach
(n = 20 variables)
www.sciencemag.org
2002
DNA chips for
massive parallel computing
by string matching
approx. 40,000 spots
2010
www.newscientist.com
algorithmic self−assembly
for cellular automaton and
universal DNA computer
2014
PLoS Biology
In-vitro Molecular Computing Based on DNA Strands Thomas Hinze
Motivation Operations on DNA Solution to Knapsack Problem Perspectives
International Molecular Computing Community
≈ 500 researchers worldwide, conference series like CMC, DNA, UC, . . .In-vitro Molecular Computing Based on DNA Strands Thomas Hinze
Motivation Operations on DNA Solution to Knapsack Problem Perspectives
Take Home Message
Living organisms comprise almost perfectDNA-based computers. We are going to learn
and to adapt the underlying principles forutilisation in vitro. There are first successes but
there is still a lot of work to do.
Further and more detailed information
• T. Hinze, M. Sturm. Rechnen mit DNA -Eine Einführung in Theorie und Praxis.De Gruyter, eBook, 2014
• T. Hinze. Computer der Natur.bookboon.com, eBook (for free), 2013
In-vitro Molecular Computing Based on DNA Strands Thomas Hinze
Motivation Operations on DNA Solution to Knapsack Problem Perspectives
Take Home Message
Living organisms comprise almost perfectDNA-based computers. We are going to learn
and to adapt the underlying principles forutilisation in vitro. There are first successes but
there is still a lot of work to do.
Further and more detailed information
• T. Hinze, M. Sturm. Rechnen mit DNA -Eine Einführung in Theorie und Praxis.De Gruyter, eBook, 2014
• T. Hinze. Computer der Natur.bookboon.com, eBook (for free), 2013
In-vitro Molecular Computing Based on DNA Strands Thomas Hinze