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

Molecular Computing: Challenges across the two tracks in

Theoretical Computer Science

Masami Hagiya

Outline

• Japanese Molecular Computer Project– Adleman-Lipton Paradigm and Improvements

• Suyama’s Dynamic Programming DNA Computer

– Autonomous Molecular Computing• Sakamoto’s 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

• 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

JSPS Project on Molecular Computing

Goals of Molecular Computing• Analyses and Applications of Computational Power of Bio

molecules– 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

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

Major Achievements of the Project• Suyama’s Dynamic Programming DNA Computers

– reduction of molecules by breadth-first search

– automation by robots

• Sakamoto’s Hairpin Engines– Whiplash PCR and SAT Engine

– molecular computation by hairpin formation

– autonomous molecular computation

• Theoretical Studies by Yokomori’s Group• Nishikawa’s Simulator for DNA computations• Arita’s New Tool for Code Design• Husimi’s 3SR-Based Evolutionary Reactor• Yamamura’s Aqueous Computing (with Head)

Dynamic ProgrammingDNA Computers

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

cf. Hamiltonian Path Problem by Adleman

Suyama’s 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

DP algorithm for 3CNF-SAT on DNA Computers

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On Scaling Up the Size of Computations

• Suyama’s 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, …

Robot for DNA Computing Based on MAGTRATIONTM

Automatic Operation of get Command on DNA Computer Robot

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Programming in DNA Computer

Hairpin Engines

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

– Winfree’s DNA Tile

– Sakamoto’s Hairpin Engines• Whiplash PCR and SAT Engine

• Applications:– Nanotechnology, Nanomachine

– (Computationally Inspired) Biotechnology

cf. Winfree’s DNA Tile

cf. Winfree’s DNA Tile

cf. Winfree’s DNA Tile

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

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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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.

6-Variable 10-Clause Formula

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Solution of a6-Variable 10-Clause formula

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)-Stepe.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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Analysis of Computational Power of Molecules

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

Some Classical Results• Reif (SPAA’95)

– 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 PSP

ACE.

• Rooß and Wagner (I&C, 1996)– Exactly the problems in PNP=p

2 can be solved in polynomial time using Lipton’s model.

Yield and Error in Reactions• Yield

– equilibrium --- equilibrium constant (K)– time to reach equilibrium

--- reaction constant (k)– example: A

[B] = (K/(1+K))(1e(k+k1

) t )

K = k/k1

• Error– example: mis-hybridization– Error probability is never zero.

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 go

od encoding.

Some Analyses• Karp, Keynon and Waarts (SODA’96)

– The number of extract operations required for achieving error-resilient bit evaluation is (loglog).

• Kurtz (DNA2, 1996)– thermodynamical analysis of path formation in Adlema

n’s experiment– time needed to form a Hamiltonian path --- (n2)

• Winfree (1998, Ph.D. Thesis)– thermodynamical analysis of DNA Tiling

• Rose, et al. (GECCO’99)– Computational Incoherency (thermodynamical analysis

of mis-hybridization)

Efficiency of SAT Engine:Tentative Analysis

• Parameters– n : number of clauses– : the probability that a satisfying assignment

cannot be detected

• Orders– Time O(n2.5)– Number of Molecules

O(4n ln(1/))

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.

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

Towards New Computational Paradigms

New Computational Paradigms

• Molecular Computing

• Chemical Computing

• Crystal Computing

• Cell Computing

• Gel Computing

• Amorphous Computing

• …

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.

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

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

Recent Results in Computation by Self-Assembly

• Rothemund and Winfree (STOC 2000)– For any f (N) non-decreasing unbounded compu

table 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.

Computation with Membranes

• Computation with Compartments– Chemical IC (MEMS)– Liposomes– P Systems (Paun)– Concurrency Calculi

• chemical abstract machine, -calculus, join calculus

• ambient calculus

• Computation by Cells• computation by gene regulation, signal transduction,

and metabolism

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)

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)

Challenges

• New Computational Paradigms

• New Computational Models

• New Programming Languages

• New Applications

• These challenges should be simultaneously attacked with the progress of implementation techniques.