It is not that the bear dances so well, it is that he dances at all. - PowerPoint PPT Presentation

“It is not that the bear dances so well, it is that he dances at all”. - L. Adleman, in reference to DNA computing CPSC 607 – Winter 2004 Eric Yeung Eric Yeung

DN NA A D •Deoxyribonucleic Acid • Genetic material of all cellular organisms and most viruses. • Carries information required for protein synthesis and replication. • DNA is organized on chromosome located in the nucleus of the cell.

DNA Structure DNA Structure • double helix structure • twisted like a winding staircase • strands composed of chemical compounds called nucleotides .

Nucleotides Nucleotides Nucleotides Nucleotides Each nucleotides consists of 3 units • a sugar molecule called deoxyribose • a phosphate group • 1 of 4 different nitrogen compounds Adenine Thymine Cystosine Guanine • each nucleotide is paired in a complementary fashion A <> T G <> C

Founders of DNA Founders of DNA James D. Watson James D. Watson • •American biochemist American biochemist Francis Crick Francis Crick • British biophysicist British biophysicist •

Watson & Crick Watson & Crick • In 1953 James Watson, left, and Francis Crick, right, described the structure of the DNA molecule as a double helix, somewhat like a spiral staircase with many individual steps. • In 1962 Crick, and Watson received the Nobel Prize for their pioneering work on the structure of the DNA molecule.

Inventor of DNA Computing Inventor of DNA Computing Leonard M. Adleman • Professor of Computer Science • Professor of Molecular Biology • University of Southern California In 1994, published a paper in Science describe how he used DNA to compute a solution to the “traveling salesman problem”

Cracking Encryptions Cracking Encryptions Three researchers • Richard J Lipton • Daniel Boneh • Christopher T Dunworth • Outlined a way for a DNA computer to crack messages encrypted with the US government’s own data encryption standards (DES). • Messages like classified telephone conversations and data transmissions between banks and the Federal Reserve.

Cracking Encryptions ( Cracking Encryptions (con con’ ’t t) ) • The coding relies on one of the 72 quadrillion “keys” •Testing all possible keys on an electronic computer would take an enormous amount of time. • However, DNA computer could test all of the keys at the same time.

DES overview DES overview • encrypts 64 bit plain text into 64 cipher text using a 56 bit key. DES( M, k ) == encryption of plain text M using the key k • run the DES circuit on a fixed 64 bit string M using all possible keys k f ( k ) = DES( M, k ) for all possible k • decryption is denoted by DES -1 That is, if E = DES( M, k ), then M = DES -1 ( E, k ).

DES circuit diagram DES circuit diagram DES circuit DES circuit • 16 levels called rounds • circuit diagram shows first 4 rounds and last • the high order 32 bits denoted by M h • the low order 32 bits denoted by M l

DES circuit con con’ ’t t DES circuit P-box • permutes the bits of its input • Suppose a P-box contains x bits and the output contains y bits • If x = y , then the box permutes the bits of the input e.g. swap 2 nd and 3 rd bits, mapping 001 to 010 • If x > y , then the box outputs a subset of bits of the input in some order • If x < y , then the box replicates some of the bits of the input to obtain a y bit output However, they found the P-box to be insignificant and may be ignored.

DES circuit con con’ ’t t DES circuit S-box • takes 48 bits of input and outputs 32 bits • 8 groups of 6 bits each • 6 bits into a lookup table and outputs 4 bits

DNA notations DNA notations • Represent strings over the alphabet {A, C, G, T} • Strings, not a strand • no orientation • strings concatenated • Watson-Crick complement of x • Reverse of a string x • Reverse & complement of a string x • Single DNA strand, from 5’ to 3’ • complement of above, from 3’ to 5’ • x as a double strand

Biological Operations Biological Operations Extract • If we want all strands containing • simply create strands of • will anneal to • A wash procedure will whisk away all strands that did not anneal Polymerization via DNA Polymerase Amplification via PCR • already discussed in class

Representing Binary Strings Representing Binary Strings • Let x = x 1 … x n be an n -bit binary string • The idea is to assign a unique 30-mer, a special primer, to each bit position and bit value. • let B i (0) be the 30-mer used to encode the i -th bit of x is 0. • for i = 0 , ..., n let S i be a 30-mer as a separator between consecutive bits. • The DNA strand representing the binary string • For convenience, given an n -bit string x , we denote by R i ( x ) the string encoding x at position i

Operations on Binary Strings Operations on Binary Strings • Let T be a test tube containing a collection of DNA strands which represent some binary strings. • Suppose we wish to extract all strands in T whose i th bit is 1. • This operation is denoted by; Extract ( T , x i = 1) • The operation can be expanded to; Extract ( T , x i x i+1 = 10) • where we extract strands in T that has 1 at i th position and a 0 at the ( i+1) th More possible operations; • Extract ( T , x i x i+1 x i+2 = 100 or x i x i+1 x i+2 = 101 ) • Extract ( T , x i x i+1 x i+2 = 100 and x i+9 x i+10 x i+11 = 111 )

Plan of DES attack Plan of DES attack • Given a message M it is possible to create a solution that contains for each k _ {0, 1} 56 a DNA strand of the form; _ S 0 R 1 ( k ) R 57 ( DES( M, k ) ) • Each strand in this solution encodes a key k and the encrypted message of M using the key k • Let ( M, E ) be a ( plain text, cipher-text ) pair. We wish to find a key k s.t. M = DES -1 ( E, k ) 1. Create the solution DES -1 ( E ) where _ S 0 R 1 ( k ) R 57 ( DES -1 ( E, k ) ) 2. Extract from DES -1 ( E ) all strands that contain the patter R 57 ( M ) 3. The extracted strands encode pairs of strings ( k, M ) where M = DES -1 ( E, k ). The key k can be recovered by sequencing any of the extracted DNA strands.

Plan of DES attack (con con’ ’t t) ) Plan of DES attack ( • Steps 2 and 3 can be done very quickly. • Laborious part is step 1. • Once the solution DES -1 ( E 0 ) is generated for some 64 bit E 0 , any DES system can be broken into.

DNA Logic Gates DNA Logic Gates In 1997, at the First International Conference on Computational Molecular Biology • Animesh Ray and Mitsu Ogihara, scientists at the University of Rochester, announced that they had built the first DNA computer hardware ‘ever’: logic gates made out of DNA. • using only the most commonplace biological laboratory techniques, such as DNA ligation and gel electrophoresis. • unlike today’s computers, DNA logic gates do not rely on electrical signal; but rather on DNA codes.

DNA Logic Gates ( DNA Logic Gates (con con’ ’t t) ) • They detect fragments of genetic material as input. • Splicing fragments together to form a single output. For example, a genetic ‘AND’ gate links two DNA inputs by chemically binding so they are locked in an end-to-end structure, just like the lego below.

DNA Logic Gates (con con’ ’t t) ) DNA Logic Gates ( • one of the first to consider whether DNA computers might be used for problems now routinely done by electronic computers, and to emulate the way electronic computers "think." • DNA computers using these logic gates are more efficient that today’s digital computers. • instead of running DNA strands through slow gel electrophoresis, • labeled strands can be added to a DNA chip, where many different known strands of DNA can bind with the complementary sequence • scientists can use the labeled strands to detect the answer more quickly

MAYA MAYA M olecular A rray of Y ES and A NDANDNOT gates • Milan Stojanovic – Columbia University • Darko Stefanovic – University of New Mexico • fashioned a device that uses DNA to play tic-tac-toe • device is made of 9 wells, contains solutions of DNA • DNA in the wells act like logic gates • As long as the automaton makes the first move, it cannot be beaten. • DNA in the wells act like logic gates

MAYA (con con’ ’t t) ) MAYA ( • contains 24 logic gates distributed in the nine wells of solution. • logic gates perform Boolean calculation when oligonucleotides are added • addition triggers an enzyme to react with DNA • the reaction exposes a fluorescent molecule, which makes the well glow to indicate the move. Mealy Automaton • like a DFA • takes an input a and outputs w

MAYA (con con’ ’t t) ) MAYA (

MAYA (con con’ ’t t) ) MAYA ( Game Tree

MAYA (con con’ ’t t) ) MAYA ( • automaton always makes the first move, (square 5) • human player always start in square 1 or 4 • 19 possible games • 10 end in victory for the automaton after 2 human moves • 7 after 3 moves • 1 after 4 moves • 1 game ends in a draw

MAYA (con con’ ’t t) ) MAYA ( • unlike the Adleman-Lipton paradigm, MAYA is not trying to use DNA’s massive parallelism • Their approach is silicomimetic • use molecules that behave as logic gates, and arrange these logic gates into more complicated circuits by mixing them in solution