DNA Computing By Thierry Metais Email: metais@enst.fr

Introduction to DNA: The life’s molecule:

Introduction: What is DNA computing ? Around 1950 first idea (precursor Feynman) First important experiment 1994: Leonard Adleman Molecular level (just greater than 10-9 meter) Massive parallelism. In a liter of water, with only 5 grams of DNA we get around 1021 bases ! Each DNA strand represents a processor ! 1/ there are two words > _ DNA a molecule that has an important place in the life process.. However in this context we must consider it as a mere molecule with interesting aspects _ computing… computing research aims at make computations “efficiently”, so in this context parallel computing is born which purpose is to do several computations in the same time by distributing them on several processors. Nevertheless nowadays the biggest parallel computer has at most 2000 processors running simultaneously… For common people this would be large enough but to solve some problems, it appears to be insufficient. In the 50ies Richard Feynman the physicist spoke about doing some computations on a molecular level The molecular computing had to wait almost 50 years to get the first real proof of its validity with the experiment of Adelman in 1994.

A bit of biology The DNA is a double stranded molecule. Each strand is based on 4 bases: Adenine (A) Thymine (T) Cytosine (C) Guanine (G) Those bases are linked through a sugar (desoxyribose) IMPORTANT: The linkage between bases has a direction. There are complementarities between bases (Watson-Crick). (A) (T) (C)(G)

DNA manipulations: If we want to use DNA as an information bulk, we must be able to manipulate it . However we are talking of handling molecules… ENZYMES = Natural CATALYSERS. So instead of using physical processes, we would have to use natural ones, more effective: for lengthening: polymerases… for cutting: nucleases (exo/endo-nucleases)… for linking: ligases… Serialization: 1985: Kary Mullis  PCR Thank this reaction we get millions of identical strands, and we are allowed to think of massive parallel computing. PCR stands for polymerase chain reaction.

And what now ? Situation: Molecular level. Lots of “agents”. (strands) Tools provided by nature. (enzymes) How can we use all this? If there is a utility …

Coding the information: 1994: THE Adleman’s experiment. Given a directed graph can we find an hamiltonian path (more complex than the TSP). In this experiment there are 2 keywords: massive parallelism (all possibilities are generated) complementarity (to encode the information) This experiment proved that DNA computing wasn’t just a theoretical study but could be applied to real problems like cryptanalysis (breaking DES ). DES = most widely used crypto system > IBM

Adleman experiment: Each node is coded randomly with 20 bases. Let Si be a code, h be the complementarity mapping. h(ATCG) = TAGC. Each Si is decomposed into 2 sub strands of length 10: Si = Si’ Si’’ Edge(i,j) will be encode as h(Si’’Sj’)( preserve edge orientation). Code: Input(N) //All vertices and edges are mixed, Nature is working NB(N,S0) //S0 was chosen as input vertice. NE(N,S4) //S4 was chosen as output vertice. NE(N,<=140) // due to the size of the coding. For i=1 to 5 do N+N(N, Si) //Testing if hamiltonian path Detect(N) //conclusion …

Example: 1 6 5 2 3 4 S0 S2 S5 S3 S1 S4 S6 E0-2 E2-5 E5-3 E3-1 E1-4 1 6 5 2 3 4 S0 S2 S5 S3 S1 S4 S6 E0-2 E2-5 E5-3 E3-1 E1-4 E4-6

New generation of computers? In the second part of [1], it is proven through language theory that DNA computing “guarantees universal computations”. Many architectures have been invented for DNA computations. The Adleman experiment is not the single application case of DNA computing… Application cases : DES, matrix multiplications, road coloring problem…

Stickers model: Memory complex = Strand of DNA (single or semi-double). Stickers are segments of DNA, that are composed of a certain number of DNA bases. To use correctly the stickers model, each sticker must be able to anneal only at a specific place in the memory complex.

To visualize: 1 1 1 Memory complex: Semi-double Soup of stickers: = A 1 1 1 Memory complex: Semi-double Soup of stickers: = A G C A T G A T Zoom

About a stickers machine? Simple operations: merge, select, detect, clean.  Tubes are considered (cylinders with two entries) However for a mere computation (DES): Great number of tubes is needed (1000). Huge amount of DNA needed as well. Practically no such machine has been created….  Too much engineering issues.

Why don’t we see DNA computers everywhere? DNA computing has wonderful possibilities: Reducing the time of computations* (parallelism) Dynamic programming ! However one important issue is to find “the killer application”. Great hurdles to overcome… Whereas DNA operations are slow, their overall potentials are that they can do about 1015 operations per second! (according to Richard J. Lipton) The actual growth of electronic computations is about 50% per year… so there would be a few years for DNA computing to exist. However DNA computing has huge possibilities in dealing with parallelism, especially with global memory problems, in comparison to electronic computing. Killer application: application > whose information can be easily coded in DNA computing. > that has a peculiar interest.

Operations done manually in the lab. Natural tools are what they are… Some hurdles: Operations done manually in the lab. Natural tools are what they are… Formation of a library (statistic way) Operations problems Time comsumming Library single strands > lots of stickers heating , cooling > 67 % success could be repeated it but we are far from the requirements. operations> _losses of DNA if it is partially stuck to the walls of the tube _DNA should be gently manipulated otherwise could be destroyed by the forces of mixing. _”good coding of the stickers and the memory strands” > otherwise a sticker could stick on 2 bit zones… _engineering problems… Note the books want to promote the DNA computing ….

Conclusion: The paradigm of DNA computing has lead to a very important theoretical research. However DNA computers won’t flourish soon in our daily environment due to the technologic issues. Adleman renouncement toward electronic computing. Is all this work lost ? NO !  “Wet computing” Adleman renouncement : “DNA computers are unlikely to become stand-alone competitors for electronic computers.” “We simply cannot, at this time, control molecules with the deftness that electrical engineers and physicists control electrons.”

Bibliography: DNA Computing, New Computing Paradigms. Gheorghe Paun,Grzegorz Rozenberg, Arto Salomaa DIMACS: DNA based computers Reducing Errors in DNA Computing by Appropriate Word Design. wdesign.pdf

Links: http://www.cs.wayne.edu/~kjz/KPZ/NaturalComputing.html http://dna2z.com/dnacpu/dna.html http://www.intermonde.net/adn/liens.html