Molecular Computing: Challenges across the two tracks in Theoretical Computer Science

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Molecular Computing Challenges across the two
tracks in Theoretical Computer Science

• Masami Hagiya

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Outline

• Japanese Molecular Computer Project
• Adleman-Lipton Paradigm and Improvements
• Suyamas Dynamic Programming DNA Computer
• Autonomous Molecular Computing
• Sakamotos Hairpin Engines
• Analysis of Computational Power of Molecules
• Complexity of Molecular Computation
• Molecular Computation as Randomized Algorithm
• Towards New Computational Paradigms
• Molecular, Chemical, Cell, and Amorphous
  Computing
• Importance of Engineering Viewpoint ---
  Programming

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JSPS Project on Molecular Computing

• Project Leader - Masami Hagiya (Computer Science)
• Members
• Takashi Yokomori (Computer Science)
• Masayuki Yamamura (Computer Science)
• Masanori Arita (Genome Informatics)
• Akira Suyama (Biophysics)
• Yuzuru Husimi (Biophysics)
• Kensaku Sakamoto (Biochemistry)
• Shigeyuki Yokoyama (Biochemistry)
• October 1996 - March 2001
• Funded by Japan Society for Promotion of Science
• Research for the Future Program

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Goals of Molecular Computing

• Analyses and Applications of Computational Power
  of Biomolecules
• Understanding Life from the Viewpoint of
  Computation
• computational mystery of life
• Life is computationally very efficient.
• Engineering Applications (not restricted to
  computation)
• combinatorial optimization
• (computationally inspired) biotechnology
• nanotechnology, nanomachine
• cryptography
• medical and pharmaceutical applications in the
  future
• New Computational Model, New Simulation Technology

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Related Fields

• Genome Informatics
• applying computer science techniques to analyze
  genomic information
• part of the human genome project
• the other way round
• But genome informatics is a good application area
  for molecular computing.
• Quantum Computing
• massively parallel computation by quantum
  superposition
• Artificial Life
• Artificial Molecular Evolution

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Major Achievements of the Project

• Suyamas Dynamic Programming DNA Computers
• reduction of molecules by breadth-first search
• automation by robots
• Sakamotos Hairpin Engines
• Whiplash PCR and SAT Engine
• molecular computation by hairpin formation
• autonomous molecular computation
• Theoretical Studies by Yokomoris Group
• Nishikawas Simulator for DNA computations
• Aritas New Tool for Code Design
• Husimis 3SR-Based Evolutionary Reactor
• Yamamuras Aqueous Computing (with Head)

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Dynamic ProgrammingDNA Computers
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Adleman-Lipton Paradigm

• Adleman (Science 1994)
• Solving Hamilton Path Problem by DNA
• Lipton, et al.
• Solving SAT Problem by DNA
• Massively Parallel Computation by Molecules
• Mainly for Combinatorial Optimization
• Random Generation by Self-Assembly
• solution candidate DNA molecule
• Selection by Molecular Biology Experiments
• Scaling Up ? Efforts to increase yields and
  reduce errors Robot and Chemical IC

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cf. Hamiltonian Path Problem by Adleman
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Suyamas Dynamic ProgrammingDNA Computer

• counting (Ogihara and Ray)
• O(20.4n) molecules for n-variable 3-SAT
• dynamic programming (Suyama)
• Iteration of Generation and Selection
• generation of candidates of partial solutions
• selection of partial solutions
• The order of computational complexity does not
  decrease, but the amount of necessary molecules
  is drastically reduced.
• 3-SAT

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DP algorithm for 3CNF-SAT on DNA Computers
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3-CNF SAT Solution on DP DNA Computer
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DP algorithm for 3CNF-SAT
ks loop k ranges over variable indices js
loop j ranges over clause indices if xk
is the 3rd literal of the j-th clause then
remove those assignments which satisfy
neither the 1st nor the 2nd literal
append XkF to the remaining assignments (do
similarly if Øxk is the 3rd literal)
k 3 x3
X1T X2T
X1T X2T X3F
X1F X2T
X1T X2F X3F
X1T X2F
X1F X2F
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DP algorithm for 3CNF-SAT
ks loop k ranges over variable indices js
loop j ranges over clause indices if xk
is the 3rd literal of the j-th clause then
remove those assignments which satisfy
neither the 1st nor the 2nd literal
append XkF to the remaining assignments (do
similarly if Øxk is the 3rd literal)
k 3 Øx3
X1T X2T
X1F X2T X3T
X1F X2T
X1T X2F
X1FX2F X3T
X1F X2F
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DP algorithm for 3CNF-SAT
ks loop k ranges over variable indices js
loop j ranges over clause indices if xk
is the 3rd literal of the j-th clause then
remove those assignments which satisfy
neither the 1st nor the 2nd literal
append XkF to the remaining assignments (do
similarly if Øxk is the 3rd literal)
k 4 x4
X1F X2T X3T
X1F X2F X3T
X1T X2T X3F X4F
X1T X2T X3F
X1T X2F X3F
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Implementation of Basic Operations
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On Scaling Up the Size of Computations

• Suyamas estimation
• 2x10-3 g of DNA for 100-variable 3-SAT
• 2x1012 g of DNA by Adleman-Lipton
• Current status 4-variable 10-clause 3-SAT
• Project goal 30-variable 100-clause 3-SAT
• Ultimate goal 100-variable 400-clause 3-SAT
• Still, 100 variables are not many.
• A number of breakthroughs (in algorithms and
  experimental techniques) are required to defeat
  electronic computers. Robots, for example,

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Robot for DNA Computing Based on MAGTRATIONTM
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Automatic Operation of get Command on DNA
Computer Robot
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Programming in DNA Computer
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Hairpin Engines
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Autonomous Molecular Computing

• Adleman-Lipton Paradigm
• generation of candidates autonomous reaction
• selection of solutions many operations from
  outside
• One-Pot Reaction ? Autonomous Computation
• Comutation by Successive Autonomous Reactions by
  Molecules
• Winfrees DNA Tile
• Sakamotos Hairpin Engines
• Whiplash PCR and SAT Engine
• Applications
• Nanotechnology, Nanomachine
• (Computationally Inspired) Biotechnology

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cf. Winfrees DNA Tile
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cf. Winfrees DNA Tile
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cf. Winfrees DNA Tile
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Hairpin Engines

• Molecular Computation by Hairpin Formation
• Hairpin --- Typical Secondary Structure
• Whiplash PCR
• DNA Automaton State Machine by DNA
• 5 Transitions in a Control Experiment
• SAT Engine
• Selection by Hairpin Structures of DNA
• 3-SAT 6-Variable 10-Clause Formula

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SAT Engine

• Sakamoto et al., Science, May 19, 2000.
• Selection by Hairpin Structures of DNA
• digestion by restriction enzyme
• exclusive PCR
• 3-SAT
• ssDNA consisting of literals, each selected from
  a clause
• complementary literal complementary sequence
• detection of inconsistency ? hairpin
• The essential part of the SAT computation is done
  by hairpin formation.
• Autonomous Molecular Computation

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(a?b?c)?(?d?e??f)? ?(?c??b?a)? ...
e
b
?b
digestion by restriction enzyme exclusive PCR
b
?b
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Selection by Hairpin Structures

• Digestion by Restriction Enzyme
• Hairpins are cut at the restriction site inserted
  in each literal sequence.
• Exclusive PCR
• PCR is inefficient for hairpins.
• In exclusive PCR, solution is diluted in each
  cycle to keep the difference in amplification.
• The number of steps is independent on the number
  of variables or clauses.

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Generation of Random Pool
(a?b?c)?(d?e?f)?(g?h?i)?(j?k?l)
a
d
g
j
Chemically Synthesized
b
e
h
k
c
f
i
l
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Generation of Random Pool
(a?b?c)?(d?e?f)?(g?h?i)?(j?k?l)
a
d
g
j
b
e
h
k
c
f
i
l
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Generation of Random Pool
(a?b?c)?(d?e?f)?(g?h?i)?(j?k?l)
a
j
h
f
d
b
i
l
g
e
k
c
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Generation of Random Pool
BstXI
BstXI
BstNI
BstNI
BstNI
4
5
5
5
4
4
4
4
4
4
9
8
4
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6-Variable 10-Clause Formula
(a?b?!c)?(a?c?d)?(a?!c?!d)?(!a?!c?d)? (a?!c?e)?(a?
d?!f)?(!a?c?d)?(a?c?!d)? (!a?!c?!d)?(!a?c?!d)
! ?
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Solution of a6-Variable 10-Clause formula
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Whiplash PCR

• DNA Automaton State Machine by DNA
• Polymerization of Hairpin
• Polymerization Stop
• Autonomous MIMD Computation of Boolean µ-formulas
• Solving NP-Complete Problems in O(1)-Step
• e.g., vertex cover
• vertex cover candidate transition table
  ssDNA
• vertex cover transition table that reaches
  the final state
• 5 Transitions in a Control Experiment

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Whiplash PCR
B
x
a
b
C
x
B
A
x
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Whiplash PCR
B
C
x
B
A
x
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Whiplash PCR
a
x
x
B
A
x
C
B
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Whiplash PCR
a
b
c
x
x
B
A
x
C
B
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(No Transcript)
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5 Transitions ina Control Experiment
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7
6
5
4
3
2
1
0
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Analysis of Computational Power of Molecules
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Complexity of Molecular Computation

• Time
• Number of Laboratory Operations
• Time for Each Operation
• more essential for the analysis of the
  computational power of molecules
• Space ( Parallelism)
• Number of Molecules
• maximum number
• total number
• Size (Length) of Molecules
• Analysis of the Trade-Off

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Some Classical Results

• Reif (SPAA95)
• A nondeterministic Turing machine computation
  with input size n, space s and time 2O(s) can be
  executed in our PAM Model using O(s) PA-Match
  steps and O(s log s) other PAM steps, employing
  aggregates of length O(s).
• Beaver (DNA1, 1995)
• Polynomial-step molecular computers compute
  PSPACE.
• Rooß and Wagner (IC, 1996)
• Exactly the problems in PNPDp2 can be solved in
  polynomial time using Liptons model.

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Yield and Error in Reactions

• Yield
• equilibrium --- equilibrium constant (K)
• time to reach equilibrium --- reaction
  constant (k)
• example A B
• B (K/(1K))(1-e-(kk-1) t )
• K k/k-1
• Error
• example mis-hybridization
• Error probability is never zero.

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Reduction of Errors

• Iteration of Laboratory Operations
• increase in computation time
• increase in loss of molecules
• increase in number of molecules
• Reduction of Error Probability
• appropriate conditions
• temperature, salt concentration
• Low temperature leads to frequent
  mis-hybridzation.
• However, high temperature decreases the yield.
• good encoding
• A number of papers have been published for
  designing good encoding.

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Some Analyses

• Karp, Keynon and Waarts (SODA96)
• The number of extract operations required for
  achieving error-resilient bit evaluation is
  Q(éloge dùélogg dù).
• Kurtz (DNA2, 1996)
• thermodynamical analysis of path formation in
  Adlemans experiment
• time needed to form a Hamiltonian path --- W(n2)
• Winfree (1998, Ph.D. Thesis)
• thermodynamical analysis of DNA Tiling
• Rose, et al. (GECCO99)
• Computational Incoherency (thermodynamical
  analysis of mis-hybridization)

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Efficiency of SAT EngineTentative Analysis

• Parameters
• n number of clauses
• e the probability that a satisfying assignment
  cannot be detected
• Orders
• Time O(n2.5)
• Number of Molecules O(4n ln(1/e))

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Molecular Computation and Randomized Algorithms

• Randomized Algorithms with Molecules
• Massive Parallelism
• Random Operations
• very easy to implement by chemical reactions
• Error in Non-Random Operations
• Error in non-random operations should not damage
  the error reducibility of a randomized algorithm.
• Error should be compensated by random operations.

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Some Recent Results

• Chen and Ramachandran (DNA6, 2000)
• k-SAT by Paturi et al.
• Díaz, Esteban and Ogihara (DNA6, 2000)
• k-SAT by Schöning
• Sakakibara (DNA6, 2000)
• PAC Learning of DNF Formulas
• Approximate Consistent Learning

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Towards New Computational Paradigms
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New Computational Paradigms

• Molecular Computing
• Chemical Computing
• Crystal Computing
• Cell Computing
• Gel Computing
• Amorphous Computing

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New Computational Paradigms

• Computation inside a Single Molecule
• Computation by Molecular Interactions
• Computation with Membranes
• Computation with Geometry
• Each paradigm is a rich source of computational
  power.
• They are strongly related with one another.

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Computation inside a Single Molecule

• Computation by Conformational Change (Structure
  Formation)
• Whiplash PCR (Sakamoto, et al.)
• SAT Engine (Sakamoto, et al.)
• NP-Completeness of Protein Folding (Fraenkel)
• Computation by Modification
• Stickers Model (Roweis, et al.)
• Aqueous Computing (Head and Yamamura)
• write-once molecular memory

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Computation by Molecular Interactions

• Computation by Self-Assembly
• DNA hybridization --- everywhere in DNA computing
• DNA tiling (Winfree, et al.)
• Computation by Cutting and Pasting
• restriction enzymes and ligase
• --- everywhere in DNA computing
• H Systems --- Splicing Systems (Head)
• Self-Assembly and Conformational Change
• Self-Assembling Automaton (Saitou)
• YAC (Yokomori)
• Concurrency Calculi (without Membranes)
• Abstract Chemistry in Artificial Life

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Recent Results in Computation by Self-Assembly

• Rothemund and Winfree (STOC 2000)
• For any f (N) non-decreasing unbounded computable
  functions, the number of tiles required for the
  self-assembly of an NN square is bounded
  infinitely often by f (N).
• Winfree, Eng and Rozenberg (DNA6, 2000)
• Linear assembly of string tiles can generate the
  output languages of finite-visit Turing Machines.

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Computation with Membranes

• Computation with Compartments
• Chemical IC (MEMS)
• Liposomes
• P Systems (Paun)
• Concurrency Calculi
• chemical abstract machine, p-calculus, join
  calculus
• ambient calculus
• Computation by Cells
• computation by gene regulation, signal
  transduction, and metabolism

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Computation with Geometry

• Computation with Compartments
• inside-or-outside topology
• Computation in Gel/on Surface
• two kinds of molecule immobile and mobile
• DNA Crystals --- DNA Tiling
• 2D or 3D topology (lattice)
• Amorphous Computing (Abelson, Knight and Sussman)
• 2D or 3D topology (continuous)
• Computational Particles
• generation of coordinate systems
• GPL (growth-point language)
• Cellular Computing (Weiss and Knight)

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Importance of Engineering Viewpoint ---
Programming

• Not Only Analysis but Also Synthesis
• Sharp Distinction from Previous Studies
• mathematical biology
• complex systems
• Synthesis Programming
• Design and Engineering of Artificial Systems
• Importance of Engineering Applications
• Milestones of Research
• Source of Motivations
• Not Restricted to Computation
• nanotechnology
• biotechnology (computatinally inspired
  biotechnology)

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Challenges

• New Computational Paradigms
• New Computational Models
• New Programming Languages
• New Applications
• These challenges should be simultaneously
  attacked with the progress of implementation
  techniques.