DNA Computing

1
DNA Computing

• Charles Ormsby III
• CSE 497
• 4/15/2004

2
Outline

• DNA Computing Characteristics
• Different Approaches
• Liptons Paper
• DNA Solution of Hard Computational Problems
• Practical Purposes
• Future Work/Funding
• References

3

• DNA Computing Characteristics
• (Advantages Disadvantages)

4
DNA Computation Characteristics

• Parallel Processing
• Processes all possible solutions simultaneously!
• Well kind of, but it is not instantaneous
• AND, it is a Physical Process!
• Therefore, the molecular steps required to
  process the solution set can take weeks
• But, we are finding ways improve time efficiency!
  More To Come

5
DNA Computation Characteristics

• Read/Write Rate of DNA
• DNA replication rate 500 base pairs per second
• - 10 times faster than human cells
• - Very low error rates
• But only 1000 bits/sec? Compare to the data
  throughput of an average hard drive? SLOW!!!
• Can anyone think of an advantage that DNA-based
  computers might have over the way todays PCs
  interact with memory?

http//www.arstechnica.com/reviews/2q00/dna/dna-2.
html
6
DNA Computation Characteristics

• YES, copies of the replication enzymes can work
  on DNA in parallel
• Bonus - Replication enzymes can start on the
  second replicated strand of DNA even before
  they're finished copying the first one. So
  already the data rate jumps to 2000 bits/sec
• Electric computers are incapable of such a feat!

http//www.arstechnica.com/reviews/2q00/dna/dna-2.
html
7
DNA Computation Characteristics

• Read/Write Rate of DNA (contd)
• Look what happens after each replicating
  iteration
• number of DNA strands increases exponentially
• 2n after n iterations
• Data rate increases by 1000 bits/sec per strand
• After 10 iterations, replication rate 1Mbit/sec
• And, after 30 iterations it increases to 1000
  Gbits/sec
• This is well beyond the sustained data rates of
  the fastest hard drives!!!

http//www.arstechnica.com/reviews/2q00/dna/dna-2.
html
8
DNA Computation Characteristics

• Data density A, T, C, G
• Bases spaced every 0.35 nanometers
• 1-dimension 18 Mbits per inch
• 2-dimension Over one million Gbits per square
  inch (assuming one base per square nanometer)
• Typical high performance hard drive
• data density 7 Gbits per square inch
• A factor of over 100,000 smaller!!

http//www.arstechnica.com/reviews/2q00/dna/dna-2.
html
9
DNA Computation Characteristics

• Double stranded nature
• - Every DNA sequence has a natural complement
• If S ATTACGTCG
• S TAATGCAGC, its complement
• DNAs complementary nature makes it a unique data
  structure for computation and can be exploited in
  many ways, such as Error Correction

10
DNA Computation Characteristics

• DNA Error Rates
• Biological error rate 1/109 copied bases
• Hard drive read error rate 1/1013
• Error Correction Errors occur due to many
  factors, for examples
• Incorrect insertions/deletions
• Damage from thermal energy and UV energy from the
  sun
• However, if the error occurs in one of the
  strands of double stranded DNA, repair enzymes
  can restore the proper DNA sequence by using the
  complement strand as a reference.
• RAID 1 array

http//www.arstechnica.com/reviews/2q00/dna/dna-1.
html
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DNA Computation Characteristics

• The Statistics of Randomness
• Pertaining to Adlemans method
• All HDPPs paths are equally likely to be formed
  during the random production of sequences
• In other words, over a large well distributed
  solution set, all solutions (or at least a great
  majority) should be present
• This is key because in order for the DNA
  computer to arrive at the correct solution, the
  solution must first exist in the solution set
• Statistics If only 99 of the solutions exist
  in the solution set than the method will have a
  successrate of only?

12

• Different Approaches
• Free Floating vs. DNA Chips

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Free Floating

• Approach 1 Bits of DNA float freely in a test
  tube
• (pioneered by Leonard M. Adleman)

14
Free Floating

• Advantages
• - Strong general problem solving application
• - Increased freedom in experimentation
• i.e. Immediate scalability by amplification
• (could the freedom also be also considered a
  disadvantage?)
• - Can encode unique problems
• - Scales very well
• Can you think of any other advantages?

HAHA, neither could I
15
DNA-based Chips

• Approach 2 A gold-plated square of glass (one
  inch square) anchors as many as a trillion
  individual strands of DNA to the glass.
• Microarrays

http//www.dhgp.de/ethics/ethics02.html
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DNA-based Chips

• Advantages
• - Easier to handle, specific orientation
• - Keeps out impurities
• - Serves as a building block to scale upwards
• - Programmable interfaces (in the future)
• - Very useful for storing information about
  Bio-agents
• Business Quiz
• Why is this approach more appealing to
  corporations and institutions who fund research?

17
DNA-based Chips

• Can be manufactured!!!

18

• Liptons Paper
• DNA Solution of Hard Computational Problems
• Lipton, Richard J., DNA Hard Solution of
  Computational Problems. Science, New Series, Vol.
  268, No. 5210 (April 28, 1995), 542-545

19
Richard Liptons DNA Solution of Hard
Computational Problems

• Two factors limit any computers performance
• Parallel processing capabilities
• 3 grams of water ? 1022 molecules
• Computations per unit time
• 100 million instructions per second
• Human Time vs. Computation Time

Lipton, Richard J., DNA Hard Solution of
Computational Problems. Science, New Series, Vol.
268, No. 5210 (April 28, 1995), 542-545
20
Richard Liptons DNA Solution of Hard
Computational Problems

• State-of-the-Art Supercomputer
• 100 million instructions per second
• Biological computers are limited to only a
  fraction of an experiment per second
• Doesnt the complexity of the experiment
  determine the difference?
• However, DNA computers counter the instruction
  time disparity with parallelism

Lipton, Richard J., DNA Hard Solution of
Computational Problems. Science, New Series, Vol.
268, No. 5210 (April 28, 1995), 542-545
21
Richard Liptons DNA Solution of Hard
Computational Problems

• Traveling Salesman Revisited
• Conventional computer can solve tour with 70
  cities, but would fail with 100 or more cities
• Even with 1023 parallel processors, Brute force
  is too inefficient
• However, are DNA computers only advantageous for
  problems with very large solutions sets?
• No, Adelmans work can be extended to produce
  solutions to all problems that are obtainable and
  unobtainable by traditional CPUs in much less time

Lipton, Richard J., DNA Hard Solution of
Computational Problems. Science, New Series, Vol.
268, No. 5210 (April 28, 1995), 542-545
22
Richard Liptons DNA Solution of Hard
Computational Problems

• NP-complete ? The Satisfaction Problem
  (SAT)
• SAT is a simple search problem, and was one of
  the first NP-complete problems
• Consider
• F (x V y) ? (Gx V Gy)
• Current Best Method test all 2n solutions for
  n variables

Lipton, Richard J., DNA Hard Solution of
Computational Problems. Science, New Series, Vol.
268, No. 5210 (April 28, 1995), 542-545
23
Richard Liptons DNA Solution of Hard
Computational Problems

• Truth Table
• Current Best Method test all 2n solutions for
  n variables

Lipton, Richard J., DNA Hard Solution of
Computational Problems. Science, New Series, Vol.
268, No. 5210 (April 28, 1995), 542-545
24
Richard Liptons DNA Solution of Hard
Computational Problems

• Initial Assumptions/Conditions
• This model is simple and idealized
• Ignores many known complex effects, but is an
  excellent first order approximation
• Strands of DNA are just sequences
• a1,, ak of the set A,C,G,T
• Double stranded DNA are a pair of sequences
• For i 1,,k given a1,, ak and b1,, bk both
  sequences of the set A,C,G,T a1 must
  complement b1, meaning A??T or C??G
• Only consider strands with a length of 20
  nucleotides

Lipton, Richard J., DNA Hard Solution of
Computational Problems. Science, New Series, Vol.
268, No. 5210 (April 28, 1995), 542-545
25
Richard Liptons DNA Solution of Hard
Computational Problems

• Five Simple operations the can be performed on
  test tubes that contain DNA strands
• Possible to synthesize a large number of copies
  of any single strand
• Annealing produces a double strand from a single
  strand and its complementary strand
• Given a test tube of DNA, one can extract a
  strand that contains some simple pattern of
  length l
• Using a Polymearse Chain Reaction (PCR), one can
  detect whether there are DNA strands at all in
  the test tube
• All of the DNA in the test tube may be amplified
  by replicating the strands in the test tube

Lipton, Richard J., DNA Hard Solution of
Computational Problems. Science, New Series, Vol.
268, No. 5210 (April 28, 1995), 542-545
26
The Theory

• One fixed test tube
• The set in the test tube corresponds to the
  following graph Gn

Lipton, Richard J., DNA Hard Solution of
Computational Problems. Science, New Series, Vol.
268, No. 5210 (April 28, 1995), 542-545
27

• All paths the travel from a1 to an 1 encode an
  n-bit binary string
• At each stage, a path has exactly two choices
• Unprimed node encodes a 1
• Primed node encodes a 0
• Therefore, the example path a1xa2ya3 encodes 01

Lipton, Richard J., DNA Hard Solution of
Computational Problems. Science, New Series, Vol.
268, No. 5210 (April 28, 1995), 542-545
28
The Solution Set Discovery

• Encode graphs vertices in DNA
• Encode edges in DNA
• 3) Encode starting and ending points in DNA

Lipton, Richard J., DNA Hard Solution of
Computational Problems. Science, New Series, Vol.
268, No. 5210 (April 28, 1995), 542-545
29
Step 1 - vertices in DNA

• The Graph is encoded in a test tube of DNA
• Each vertex of the graph is assigned a random
  pattern of length l from A,C,G,T
• Each encoding is referred to as the name of the
  vertex and is comprised of two parts
• 1st half ? pi
• 2nd half ? qi
• Therefore, each vertex can be referenced by piqi

Lipton, Richard J., DNA Hard Solution of
Computational Problems. Science, New Series, Vol.
268, No. 5210 (April 28, 1995), 542-545
30
Step 2 - edges in DNA

• Then, fill a test tube with the following
• For each vertex, add many copies of a 5 ? 3
  DNA sequence of the form piqi
• For each edge i ? j, put many copies of a 3 ?
  5 sequence that is of the form (GqjGpi)
• If
• Vertex i ATCGGCTACTCCTGACTTGA
• pi ATCGGCTACT
• qi CCTGACTTGA
• Vertex j AGGTTCAGTCAGGCCTATTC
• pi AGGTTCAGTC
• qj AGGCCTATTC
• Therefore, for edge I ? j a sequence like the
  following would be added
• Gqj GGACTGAACT Gpi TCCAAGTCAG

Lipton, Richard J., DNA Hard Solution of
Computational Problems. Science, New Series, Vol.
268, No. 5210 (April 28, 1995), 542-545
31
Step 3 end points in DNA

• Then, add the following DNA strands
• Add a 3 ? 5 sequence of length l /2 that is
  complementary to the first half of the initial
  vertex
• Similarly, add 3 ? 5 sequence of length l /2
  that is complementary to the last half of the
  final vertex
• In other words, add Gp1 Gqn)
• If initial vertex was
• ACTTGCCATCTCCGATACTT
• And the final vertex was
• TCGCCTAATCTACGATCTTA
• then add
• TGAACGGTAG ATGCTAGAAT

Lipton, Richard J., DNA Hard Solution of
Computational Problems. Science, New Series, Vol.
268, No. 5210 (April 28, 1995), 542-545
32
Goal of Initial Solution Set

• KEY That every legal path in Gn corresponds to
  a correctly matched sequence of vertices and
  edges
• Any path through the graph must contain a
  sequence that alternates between vertex, edge,
  vertex, edge,...
• Try this visual
• Consider the edge v ? u, any path that passes
  through v and then passes through u must fit
  together like bricks

Lipton, Richard J., DNA Hard Solution of
Computational Problems. Science, New Series, Vol.
268, No. 5210 (April 28, 1995), 542-545
33

• So, the top 5 ? 3 represents a series of
  vertices
• Whereas, the bottom 3 ? 5 represents an edge
• Furthermore
• Vertex v is encoded as puqv
• Edge uv is encoded as G qv G pu

Lipton, Richard J., DNA Hard Solution of
Computational Problems. Science, New Series, Vol.
268, No. 5210 (April 28, 1995), 542-545
34

• Why is this ordering significant?

Lipton, Richard J., DNA Hard Solution of
Computational Problems. Science, New Series, Vol.
268, No. 5210 (April 28, 1995), 542-545
35

• the end of the vertex and the beginning of the
  edge can anneal because they are complementary!
• Similarly, the end of the edge and the beginning
  of the next vertex can anneal too!
• High Probability of No inadvertant paths
• Sequences are chosen at random
• 2) The sequence lengths are large
• After the annealing, all of the possible paths
  through the graph will be encoded into n-bit
  long DNA sequences

Lipton, Richard J., DNA Hard Solution of
Computational Problems. Science, New Series, Vol.
268, No. 5210 (April 28, 1995), 542-545
36
Similarity Between Sequences

• At any given vertex in a path, the choice is
  simply left or right, therefore, all paths are
  similar
• What does this mean?
• All paths are equally likely to be formed
  during the random production of sequences
• In other words, over a large well distributed
  solution set, all solutions (or at least a great
  majority) should be present
• This is key because in order for the computer
  to arrive at the correct solution, the solution
  must first exist in the solution set
• Statistics!

Lipton, Richard J., DNA Hard Solution of
Computational Problems. Science, New Series, Vol.
268, No. 5210 (April 28, 1995), 542-545
37
Extraction Operations

• Notation
• E(t,i,a), denotes all sequences in test tube t
  where i a
• Perform one extract operation such that
• checks for the sequence that corresponds to the
  name of xl if a 1,
• and if a 0, it check for xl

Lipton, Richard J., DNA Hard Solution of
Computational Problems. Science, New Series, Vol.
268, No. 5210 (April 28, 1995), 542-545
38
Extraction Operations

• Construct a series of test tubes
• Values Present
• t0 contains all sets 00,01,10,11
• t1 E(t0, 1, 1) 10,11
• t1 remainder of t1 00,01
• t2 E(t1, 2, 1) 01
• Pour t1 and t2 together to form t3
• t3 t1 t2 01,10,11

Lipton, Richard J., DNA Hard Solution of
Computational Problems. Science, New Series, Vol.
268, No. 5210 (April 28, 1995), 542-545
39
Extraction Operations

• 2) Construct a series of test tubes
• Values Present
• t4 E(t3, 1, 0) 01
• t4 remainder of t4 00,10,11
• t5 E(t4, 2, 0) 10
• Pour t4 and t5 together to form t6
• t6 t4 t5 01,10

Lipton, Richard J., DNA Hard Solution of
Computational Problems. Science, New Series, Vol.
268, No. 5210 (April 28, 1995), 542-545
40
Extraction Operations

• 3) Check to see if there are DNA strands
  available in t6
• Those left in t6 are the satisfying assignment!

Lipton, Richard J., DNA Hard Solution of
Computational Problems. Science, New Series, Vol.
268, No. 5210 (April 28, 1995), 542-545
41
Understanding How it Works

• Test tube t3 consists of all the sequences that
  satisfy the first clause 01,10,11
• and, similarly t6 consists of all those that
  satisfy the second clause and are contained in t3

Lipton, Richard J., DNA Hard Solution of
Computational Problems. Science, New Series, Vol.
268, No. 5210 (April 28, 1995), 542-545
42
More General Case

• Any SAT problem on
• n variables, and
• m clauses,
• can be solved with at most m extract steps
• (with one detect step at end)
• Liptons Acknowldegments
• Operations are assumed perfect and without error

Lipton, Richard J., DNA Hard Solution of
Computational Problems. Science, New Series, Vol.
268, No. 5210 (April 28, 1995), 542-545
43

• Practical Purposes

44
Purposes

• Counter Bioterrorism/Monitor Genetic Progression
• Institute for Countermeasures against
  Agricultural Bioterrorism (ICAB)
• Plan
• 1) Obtain DNA sequences from crops, animals,
  bio-agents, etc.
• 2) Deploy DNA-chip technology to identify and
  characterize
• 3) Build geo-referenced information system
• 4) Predict and track the spread of bio-agents
  after introduction
• 5) Create powerful DNA-based tools for
  monitoring and enhanced diagnosis
• DNA microarrays DNA-based chips
• - Can store 1,000 to 100,000 different
  diagnostic DNA sequences
• Next generation will contain one million tags!

http//icab.tamu.edu/
45
Purposes

• Predictive Gene Testing

http//www.dhgp.de/ethics/ethics02.html
46

• Poker Playing

DNA Computing 7th International Workshop on DNA
Based Computers, Dna7, Tampa, Florida, June
10-13, 2001 Revised Papers
47

• Weighted-Recursive Algorithms

DNA Computing 7th International Workshop on DNA
Based Computers, Dna7, Tampa, Florida, June
10-13, 2001 Revised Papers
48
Pessimism

• 1) Too fragile and prone to error
• 2) The field is dominated by hard-core
  enthusiasts who, will be forced to "slog through
  and do the heavy research" before there is a
  major breakthrough

Optimism
However, keep in mind the first commercially
available electronic computer was not well
received, and IBM in 1951 had to reinvent what
they spent millions of dollars and years working
on to fit customers needs (such as payroll)
http//www.jsonline.com/alive/news/0607dna.stm
49
The Future of DNA Computing

• Commercial application by 2010
• Alternative to traditional computing by 2020
• Vision Today we have not one but several
  companies making "DNA chips," where DNA strands
  are attached to a silicon substrate in large
  arrays (for example Affymetrix's genechip).
  Production technology of MEMS is advancing
  rapidly, allowing for novel integrated small
  scale DNA processing devices. The Human Genome
  Project is producing rapid innovations in
  sequencing technology. The future of DNA
  manipulation is speed, automation, and
  miniaturization

http//www.jsonline.com/alive/news/0607dna.stm
50
Research Funding

• Funding
• National Science Foundation
• Pentagon's Defense Advanced Research Projects
  Agency - Much of the military's interest arises
  from the increasing sophistication of encryption
  techniques that other countries can use to encode
  their data. As a result, Washington needs
  ever-more-powerful computers for code breaking

51

• Internet References
• http//chronicle.com/data/articles.dir/art-44.dir/
  issue-4.dir/14a02301.htm
• http//www.jsonline.com/alive/news/0607dna.stm
• http//www.arstechnica.com/reviews/2q00/dna/dna-1.
  html
• Book/Papers References
• Lipton, Richard J., DNA Hard Solution of
  Computational Problems. Science, New Series, Vol.
  268, No. 5210 (April 28, 1995), 542-545
• DNA Computing 8th International Workshop on DNA
  Based Computers, Dna8, Sapporo, Japan, June
  10-13, 2002 Revised Papers (Lecture Notes in
  Computer Science, 2568)
• DNA Computing 7th International Workshop on DNA
  Based Computers, Dna7, Tampa, Florida, June
  10-13, 2001 Revised Papers
• Future References
• http//www.nas.nasa.gov/
• http//www.nas.nasa.gov/Research/Reports/reportsar
  chive.html