D DN NA A Deoxyribonucleic Acid Genetic material of all - PDF document

D DN NA A •Deoxyribonucleic Acid • Genetic material of all cellular organisms and most viruses. • Carries information required for protein “It is not that the bear dances so synthesis and replication. well, it is that he dances at all”. • DNA is organized on chromosome - L. Adleman, in reference to DNA computing located in the nucleus of the cell. CPSC 607 – Winter 2004 Eric Yeung Eric Yeung DNA Structure DNA Structure Nucleotides Nucleotides Nucleotides Nucleotides Each nucleotides consists of 3 units • double helix structure • a sugar molecule called deoxyribose • twisted like a winding staircase • a phosphate group • 1 of 4 different nitrogen compounds • strands composed of chemical compounds Adenine Thymine called nucleotides . Cystosine Guanine • each nucleotide is paired in a complementary fashion A <> T G <> C Founders of DNA Founders of DNA Watson & Crick Watson & Crick James D. Watson James D. Watson • In 1953 James Watson, left, and Francis Crick, right, •American biochemist • American biochemist 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 Francis Crick Francis Crick their pioneering work on the structure of the DNA molecule. • British biophysicist British biophysicist •

Inventor of DNA Computing Inventor of DNA Computing Cracking Encryptions Cracking Encryptions Leonard M. Adleman Three researchers • Professor of Computer Science • Professor of Molecular Biology • Richard J Lipton • University of Southern California • Daniel Boneh • Christopher T Dunworth In 1994, published a paper in • Outlined a way for a DNA computer to crack Science describe how he used messages encrypted with the US government’s own DNA to compute a solution to data encryption standards (DES). the “traveling salesman problem” • Messages like classified telephone conversations and data transmissions between banks and the Federal Reserve. Cracking Encryptions ( Cracking Encryptions DES overview DES overview (con con’ ’t t) ) • encrypts 64 bit plain text into 64 cipher text using • The coding relies on one of the 72 quadrillion a 56 bit key. “keys” DES( M, k ) == encryption of plain text M using the key k •Testing all possible keys on an electronic • run the DES circuit on a fixed 64 bit string M using all possible keys k computer would take an enormous amount of f ( k ) = DES( M, k ) for all possible k time. • decryption is denoted by DES -1 • However, DNA computer could test all of the keys at the same time. That is, if E = DES( M, k ), then M = DES -1 ( E, k ). DES circuit diagram DES circuit diagram DES circuit con DES circuit con’ ’t t DES circuit DES circuit P-box • permutes the bits of its input • 16 levels called rounds • Suppose a P-box contains x bits and the output contains y bits • circuit diagram shows • If x = y , then the box permutes the bits of the input first 4 rounds and last e.g. swap 2 nd and 3 rd bits, mapping 001 to 010 • the high order 32 bits • If x > y , then the box outputs a subset of bits of the input denoted by M h in some order • the low order 32 bits • If x < y , then the box replicates some of the bits of the denoted by M l input to obtain a y bit output However, they found the P-box to be insignificant and may be ignored.

DES circuit con DES circuit con’ ’t t DNA notations DNA notations • Represent strings over the alphabet {A, C, G, T} S-box • takes 48 bits of input and outputs 32 bits • Strings, not a strand • 8 groups of 6 bits each • no orientation • strings concatenated • 6 bits into a lookup table and outputs 4 bits • 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 Representing Binary Strings Representing Binary Strings • Let x = x 1 … x n be an n -bit binary string Extract • The idea is to assign a unique 30-mer, a special primer, • If we want all strands containing to each bit position and bit value. • simply create strands of • let B i (0) be the 30-mer used to encode the i -th bit of x is 0. • will anneal to • for i = 0 , ..., n let S i be a 30-mer as a separator between • A wash procedure will whisk away all strands that did not consecutive bits. anneal • The DNA strand representing the binary string Polymerization via DNA Polymerase • For convenience, given an n -bit string x , we denote by R i ( x ) Amplification via PCR the string encoding x at position i • already discussed in class Operations on Binary Strings Operations on Binary Strings Plan of DES attack Plan of DES attack • Let T be a test tube containing a collection of DNA strands • Given a message M it is possible to create a solution that which represent some binary strings. contains for each k _ {0, 1} 56 a DNA strand of the form; • Suppose we wish to extract all strands in T whose i th bit is 1. _ S 0 R 1 ( k ) R 57 ( DES( M, k ) ) • This operation is denoted by; • Each strand in this solution encodes a key k and the encrypted Extract ( T , x i = 1) message of M using the key k • The operation can be expanded to; • Let ( M, E ) be a ( plain text, cipher-text ) pair. We wish to find a key k s.t. M = DES -1 ( E, k ) Extract ( T , x i x i+1 = 10) 1. Create the solution DES -1 ( E ) where _ S 0 R 1 ( k ) R 57 ( DES -1 ( E, k ) ) • where we extract strands in T that has 1 at i th position and a 0 at the ( i+1) th 2. Extract from DES -1 ( E ) all strands that contain the patter R 57 ( M ) More possible operations; 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 • Extract ( T , x i x i+1 x i+2 = 100 or x i x i+1 x i+2 = 101 ) the extracted DNA strands. • 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 (con Plan of DES attack ( con’ ’t t) ) DNA Logic Gates DNA Logic Gates In 1997, at the First International Conference on Computational Molecular Biology • Steps 2 and 3 can be done very quickly. • Animesh Ray and Mitsu Ogihara, scientists at the University of Rochester, announced that they had built the • Laborious part is step 1. first DNA computer hardware ‘ever’: logic gates made out of DNA. • Once the solution DES -1 ( E 0 ) is generated for • using only the most commonplace biological laboratory some 64 bit E 0 , any DES system can be broken techniques, such as DNA ligation and gel electrophoresis. into. • unlike today’s computers, DNA logic gates do not rely on electrical signal; but rather on DNA codes. DNA Logic Gates DNA Logic Gates ( DNA Logic Gates (con DNA Logic Gates ( con’ ’t t) ) (con con’ ’t t) ) • They detect fragments of genetic • one of the first to consider whether DNA computers might be material as input. used for problems now routinely done by electronic computers, and to emulate the way electronic computers "think." • Splicing fragments together to form a • DNA computers using these logic gates are more efficient that single output. today’s digital computers. • instead of running DNA strands through slow gel electrophoresis, For example, a genetic ‘AND’ gate links • labeled strands can be added to a DNA chip, where many two DNA inputs by chemically binding different known strands of DNA can bind with the complementary so they are locked in an end-to-end sequence structure, just like the lego below. • scientists can use the labeled strands to detect the answer more quickly MAYA MAYA MAYA (con MAYA ( con’ ’t t) ) • contains 24 logic gates distributed in the nine wells of solution. M olecular A rray of Y ES and A NDANDNOT gates • logic gates perform Boolean calculation when oligonucleotides are • Milan Stojanovic – Columbia University added • Darko Stefanovic – University of New Mexico • addition triggers an enzyme to react with DNA • fashioned a device that uses DNA to play tic-tac-toe • the reaction exposes a fluorescent molecule, which makes the well glow to indicate the move. • device is made of 9 wells, contains solutions of DNA • DNA in the wells act like logic gates Mealy Automaton • As long as the automaton makes the first move, it cannot be • like a DFA beaten. • takes an input a and outputs w • DNA in the wells act like logic gates