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DNA Computing

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DNA Computing Elements of complementary nature abound in nature. Complementary parts (in nature) can self-assemble . A universal principle? – PowerPoint PPT presentation

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Title: DNA Computing


1
DNA Computing
2
A universal principle?
  • Elements of complementary nature abound in
    nature.
  • Elements of complementary nature spontaneously
    stick together.
  • This complementary-attraction-principle seems
    to pervade many aspects of life (both molecular
    and higher levels).

3
Cells atoms that make up living things
4
DNA strings that encode the traits of living
organisms
5
Complementary-attraction in DNA
6
DNA computing Basic operations
  • Synthesize
  • Prepare large numbers of copies of any short
    single DNA strand.
  • Anneal
  • Create a double strand from complementary single
    strands.
  • Extract
  • Pull out those DNA sequences containing a given
    pattern of length l (from a test tube).
  • Detect
  • Determine whether or not there are any DNA
    strands at all in a test tube.
  • Amplify
  • Replicate all (or selectively, some) of the DNA
    strands in a test tube.

7
Hamiltonian Path Problem (HPP)
8
Adlemans experiment
9
Adlemans experiment
CITY DNA name Complement
Auckland ACTTGCAG TGAACGTC
Christ Church TCGGACTG AGCCTGAC
Wellington GGCTATGT CCGATACA
Dunedin CCGAGCAA GGCTCGTT
FLIGHT DNA flight number
Auckland-Christ Church CGTCAGCC
Auckland-Dunedin CGTCGGCT
Christ Church-Wellington TGACCCGA
Christ Church-Dunedin TGACGGCT
Christ Church-Auckland TGACTGAA
Wellington-Dunedin CCGAGGCT
10
Adlemans experiment
11
Adlemans experiment Filtering process I
Getting rid of DNA strands that dont start with
Auckland, end with Dunedin (using PCR
amplification)
12
Adlemans experiment Filtering process II
Getting rid of DNA strands that dont have
length 24 (using gel electrophoresis)
13
Adlemans experiment Filtering process III
Getting rid of DNA strands that dont have
Christ_Church Welling_ton (using probe
molecules)
14
What is a natural algorithm? (prose version)
Natural Algorithm a free means to an end
Traditionally, when computists solve problems,
they try to achieve the desired end by
painstakingly developing a suitable means---an
algorithm. On the other hand, when natural
computists solve problems, they try to discover a
natural (computing) system, one that is bound to
produce the desired end (or something close to
such an end) and whose capacity to produce such
an end is innate. (That is, the systems ability
to reach the desired end is not something the
computist deliberately assigns to it, but
something which the system has been endowed
with.) The means by which natural systems
realize an end is something that comes for
free the computist need not bother to know the
exact means by which the system would achieve the
desired end, but simply be aware of the fact that
such an end will somehow be achieved.
15
What is a natural algorithm? (poem version)
"What, my dear Sir, is a Natural Algorithm?"So
asked Boswell."Bah, that is but a simple idea",
said Dr. Johnson.An algorithm is nothing but a
means,Not as hard as it seemsOne which humans
so meticulously design---And all that, my
friend,Is for the computer---to achieve an
'end'. A natural algorithm is also a means,But
one that you get for freeAll you need, my
dear Boswell, is to seekFor when you seek, you
shall findThat piece of nature's machinery which
does what you wantBe it sorting, be it searching
or solving SAT!It's right there, neat and
clean---The end you seekJust take a
peek. "But, Sir, by what means does nature reach
its end?"Why bother, my dear Boswell,When
nature does it well.The means is but free,
andFor us (and for nature), it's the end that
matters.What matters for starters,Though, is by
one means or the other Will it reach its end!
16
Liptons SAT
(x V y) (x V y)
Possible Paths
Paths satisfying Clause-1
Paths satisfying Clause-2
17
Liptons SAT Filtering process I
Getting rid of DNA strands (paths) that do not
satisfy Clause-1
18
Liptons SAT Filtering process II
Getting rid of DNA strands (paths) that do not
satisfy Clause-2
19
Liptons SAT Filtering process I
Paths satisfying Clause 1 (x 1) OR (y 1)
20
Liptons SAT Filtering process II
Paths satisfying BOTH clauses 1 2 (x 1) OR
(y 1) AND (x 0) OR (y 0)
21
Universality of DNA computing
What does a shuffle mean? Take any two strings x
and y we can form strings by just cutting and
pasting pieces (substrings) from them in such a
way that the resulting strings will preserve the
order of letters in x and y. Call such a
resulting string a shuffle of x and y. e.g. Take
x 0011 and y 0011 00001111 is a shuffle of x
and y. But, 01100011 is not a shuffle of x and y.
Twin-Shuffle language Pick x, an arbitrary string
over the alphabet 0,1 and y, its
underscored-version. Form the shuffles of ALL
such x and y. The resulting (infinite) set of
strings is the Twin-Shuffle language.
22
Universality of DNA computing
DNA-strings Twin-Shuffle language Every DNA
double strand can be represented by a unique,
valid shuffle, i.e. a string in TS. Also, for
every string in TS, one can construct a (unique)
double stranded DNA that mirrors such a string.
In other words, the double-stranded DNA strings
and the strings in TS can be put in one-to-one
correspondence.
(DNA) Universality Theorem For every computably
enumerable language L, we can design a finite
state machine (with outputs) that can generate
exactly those strings in L when inputted with
strings from TS.
23
Universality of DNA computing
DNA-strings ?? Twin-Shuffle language Every DNA
double strand can be represented by a unique,
valid shuffle, i.e. a string in TS. Also, for
every string in TS, one can construct a (unique)
double stranded DNA that mirrors such a string.
x1 x1 x2 x2 x3 x3 x4 x4
DNA strand
shuffle
x1 x2 x3 x4 x1 x2 x3 x4
x1 x1 x2 x3 x2 x3 x4 x4
shuffle
DNA strand
24
  • References
  • E. Schrödinger, What is Life The Physical Aspect
    of the Living Cell (1944), Cambridge University
    press.
  • The Living Cell, Readings from Scientific
    American, W. H. Freeman and Company, 1965.

Thank you!
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