DNA Automata, Turing Machines and Molecular Computers

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DNA Automata, Turing Machines and Molecular
Computers

• Presenter
• Arif Raza

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Outline

• Stochastic Computing with biomolecular automata
  Shapiro and Benenson, 2004
• Bringing DNA Computers to Life Shapiro and
  Benenson, 2006
• DNA molecule provides a computing machine with
  both data and fuel Shapiro and Benenson, 2003
• Programmable and autonomous computing machine
  made of biomolecules Shapiro and Benenson, 2001
  
• An autonomous molecular computer for logical
  control of gene expression Shapiro and Benenson,
  2004
• A DNA and restriction enzyme Implementation of
  Turing Machines Paul Rothemund, 1995
• Conclusion

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Stochastic Computing with biomolecular automata
Shapiro and Benenson, 2004
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Stochastic Computing with biomolecular automata

• Biomolecular computers are autonomous
  programmable machines in which input, output,
  software and even hardware are made up of
  biological molecules.
• For biomedical tasks, a stochastic approach is
  more suitable compared to the deterministic one.

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Stochastic Computing with biomolecular automata
Contd

• In this automata, the input is encoded as a
  single DNA molecule, transition rules by another
  set of DNA molecules and the hardware by
  DNA-manipulating enzymes.
• The input molecules are processed by the hardware
  molecules under the direction of software
  molecules.
• After computation, the result is encoded as an
  output molecule.

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Stochastic Computing with biomolecular automata
Contd

• A deterministic automaton is programmed by
  selecting a set of instructions, one for each
  state symbol.
• A stochastic automaton uses all transition rules
  using predefined probability.
• Such automata are used for processing
  nondeterministic sequences.

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Stochastic Computing with biomolecular automata
Contd

• A design principle for stochastic machines using
  biomolecular computers has been shown.
• The molecular stochastic automaton was based on
  two input, two state automaton developed in a
  laboratory, thus having eight possible transition
  rules.
• While computing in a large assembly of input
  molecules, the probability to reach to a final
  state is measured by the relative concentration
  of output molecules.

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Stochastic Computing with biomolecular automata
Contd

• In a set of experiments, the concentration of the
  input was kept constant while varying the
  concentration of the competing transition
  molecules.
• The results showed that the transition
  probability is dependent on the relative
  concentration ratio, not on the absolute software
  concentration.
• Distribution of the output was predicted using
  calibration graphs, and good correlation was
  found between the predicted and the actual
  results.
• Although some systematic errors were noted.

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Stochastic Computing with biomolecular automata
Contd

• To compensate for the discrepancies, another set
  of experiments was performed, based on the
  simulation of the reaction network, using least
  square optimization method.
• The optimization was started with measured
  transition probabilities and then was refined
  iteratively till the required degree of accuracy
  was achieved.
• As required by the molecular computational model,
  for the same concentration, the transition
  probabilities were found to be the same, even for
  different programs.

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Bringing DNA Computers to LifeShapiro and
Benenson, 2006
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Bringing DNA Computers to Life

• Alan Turing, a British mathematician was the
  first one who conceived a universal computing
  machine.
• However, he imagined it as a person with
  infinitely long piece of paper, a pencil and
  instruction set.
• This imaginary person would read a symbol change
  it according to the rules and then moves on to
  the other symbol, till no more instructions are
  left.

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Bringing DNA Computers to Life Contd

• Processing of DNA and RNAs within human cells by
  molecular machines have striking similarities
  with Turing machines.
• These include processing of information in a
  string of symbols, moving step-wise along those
  symbols and adding or changing symbols according
  to given set of rules.

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Bringing DNA Computers to Life Contd

• Adleman in 1994 demonstrated the computational
  power of molecules by solving the complex
  mathematical problem of Hamiltonian path.
• He made use of molecules' pairing affinities and
  by combining trillions of them in a test tube,
  and thus managed to solve the complex problem in
  minutes.

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Bringing DNA Computers to Life Contd

• The authors of this paper started from a very
  simple Turing-like machine which could determine
  from a string of two-letter alphabet a and b,
  that it contains even number of b's or not.
• In 2001, they came up with a computer, with its
  input, software and hardware placed in a buffer
  solution in a test tube.
• It completed its processing in an automatic way.

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Bringing DNA Computers to Life Contd

• This automaton was found to be able to do
  different tasks using a mix of transition
  molecules.
• It was also found that by removing ligase, would
  not only reduce the required enzymatic hardware
  by 50, it also allowed the computer to work
  without any external fuel.

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Bringing DNA Computers to Life Contd

• By 2003, they were able to build an autonomous
  programmable computer that was able to process
  any length of molecule as an input, with fixed
  number of software and hardware molecules.
• Furthermore, this computer would never run out of
  energy.

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DNA molecule provides a computing machine with
both data and fuel Shapiro and Benenson, 2003

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DNA molecule provides a computing machine with
both data and fuel

• In this research, it is shown that a single DNA
  molecule can provide both the input data and
  everything required for a molecular automaton.
• It has been shown that software and hardware
  molecules can process any input molecule of any
  length without external energy supply.

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DNA molecule provides a computing machine with
both data and fuel- Contd

• A DNA-based finite automaton has been described
  that computes through repeated iterative
  processing.
• The self-assembly is reversible and is made
  possible by hybridization energy between
  complementary ends of software.

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DNA molecule provides a computing machine with
both data and fuel- Contd

• The proposed automaton displays the practical
  verification of the theoretical possibility to
  use the potential energy of a DNA input molecule
  to be used for a molecular computation.

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DNA molecule provides a computing machine with
both data and fuel- Contd

• This automaton is very similar in its overall
  logical structure to a hypothetical biomolecular
  computing device proposed by Bennett for a
  low-energy computing device.
• The main difference is that in Bennetts
  hypothetical device was reversible, whereas here
  the use of input destruction by this automaton
  entails entropy increase and nontrivial heat
  dissipation, making it irreversible.

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DNA molecule provides a computing machine with
both data and fuel- Contd

• It is also believed here that the design choice
  made by DNA, RNA, and proteins is important.
• Its decomposition dissipates heat and increases
  entropy.
• This design by recycling its constituent bits
  makes the cell an efficient information-processing
  device.

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Programmable and autonomous computing machine
made of biomolecules Shapiro and Benenson, 2001

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Programmable and autonomous computing machine
made of biomolecules

• The designers of molecular DNA computers have
  been inspired by the analogy of Turing machine
  and automata.
• In this paper, the authors have described an
  autonomous programmable finite automaton.

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Programmable and autonomous biomoleculer computer
Contd

• Its hardware is made up of nuclease and ligase in
  a restricted form.
• The double stranded DNA molecules are used to
  encode the software.
• The solution of these components is mixed, and
  through a flow of different (restriction,
  hybridization and ligation) cycles, the input
  molecule is processed by the automaton to produce
  the computed result as an output, as it reaches
  the final state.

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Programmable and autonomous biomoleculer computer
Contd

• The example finite automaton has two internal
  states (S0 and S1) with two input symbols a and
  b.
• Thus there are eight possible transition rules T1
  to T8, and based on which the machine makes the
  decision about which internal states it will
  accept and which it will not.

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Programmable and autonomous biomoleculer computer
Contd

• A transition molecule detects the current state
  and symbol and determines the next state.
• It consists of FokI recognition site (red) and
  spacer (green) that determines the location of
  the FokI.
• The cleavage site inside the next symbol
  encoding, in turn defines a next state.
• 1-bp spacers effect S1 to S0 transition, 3-bp
  maintain the current state, and 5-bp transfer S0
  to S1.

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Programmable and autonomous biomoleculer computer
Contd

• p GGATGTAC p GGATGACGAC
• GGT CCTACATGCCGAp GGT CCTACTGCTGCCGAp
• T1 S0 S0 T2S0 S1
• p GGATGACG p GGATGACGAC
• GGT CCTACTGCGTCGp GGT CCTACTGCTGGTCGp
• T3 S0 S0 T4S0 S1

22
22
a
a
28
15
b
b
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Programmable and autonomous biomoleculer computer
Contd

• p GGATGA p GGATGACG
• GGT CCTACTGACCp GGT CCTACTGCGACCp
• T5 S1 S0 T6S1 S1
• p GGATGG p GGATGACG
• GGT CCTACCGCGTp GGT CCTACTGCGCGTp
• T7 S1 S0 T8S1 S1

15
28
a
a
21
30
b
b
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Programmable and autonomous biomoleculer computer
Contd

• Finite automata with two states (S0 and S1) and
  two symbols (a and b).
• Diagram representing the automaton A1 accepting
  inputs with an even number of b symbols.
• Incoming unlabelled arrow represents the initial
  state, labelled arrows represent transition
  rules, and the double circle represents an
  accepting state.

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Programmable and autonomous biomoleculer computer
Contd

• FokI enzyme is the main engine of the automaton
  that recognizes a specific DNA sequence and
  cleave away from it.
• It binds the sequence
• 5' - GGATG - 3'
• 3' - CCTAC - 5'
• and cleaves the DNA both on the top and the
  bottom strand ( 9 bp and 13 bp respectively)
  thus leaving a 4-letter-long sticky-end on the
  top.

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Programmable and autonomous biomoleculer computer
Contd

• The symbols, a, b (input) and t (terminator), are
  encoded as 6bp sequences as shown below
• a
• 5' - CTGGCT - 3'
• 3' - GACCGA - 5'
• b
• 5' - CGCAGC - 3'
• 3' - GCGTCG - 5'
• t
• 5' - TGTCGC - 3'
• 3' - ACAGCG - 5'
• The input contains a restriction site for FokI,
  followed by the catenation of the encodings for
  the string abt.

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Programmable and autonomous biomoleculer computer
Contd

• Every state-symbol pair has been encoded as a
  4-mer DNA strand.
• This means that the 4-mer suffix of the encoded
  symbol represents the symbol present/read in
  state S0 and
• the 4-mer prefix of the encoded symbol means that
  the symbol is present/ read in state S1.
• Thus, to represent S0-a state-symbol pair, 4-mer
  suffix from the 6bp sequence representing a (5' -
  CTGGCT - 3') will be GGCT

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Programmable and autonomous biomoleculer computer
Contd

• 5'-GGCT - 3' represents the coding for S0-a.
• 5'-CTGG - 3' represents the coding for S1-a.
• Likewise
• 5' -CAGC - 3' represents the coding for S0-b
• 5' -CGCA - 3' represents the coding for S1-b
• And
• 5' - TCGC - 3' represents the coding for S0-t
• 3' - ACAG - 5' represents the coding for S1-t

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Programmable and autonomous biomoleculer computer
Contd

• However, the output detection molecules are of
  different lengths, which makes them easily
  distinguishable by gel electrophoresis.
• The output detection molecules S0-D is a 161-mer
  DNA double strand with an overhang 3'-AGCG-5',
  representing S0 as the final state of the
  computation.
• Whereas, S1-D is a 251-mer DNA double strand with
  an overhang 3'-ACAG-5', representing S1 as the
  final state of the computation.

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a b t
G G A T G C T G G C T C G C A G C T G T C G C
C C T A C G A C C G A G C G T C G A C A G C G
G G C T C G C A G C T G T C G C
G C G T C G A C A G C G
p G G A T G T A C G G C T C G C A G C T G T C G
C GGT C C T A C A T G C C G A G C G
T C G A C A G C G C A G C T G T
C G C A C A G C G p
G G AT G A C G A C C A G C T G T C G C
GGT C C T A C T G C T G G T C
G A C A G C G T G T C
T G T C A C A G
21
7
300
FokI
ltS0-agt
300
Ligase T1
300
22
FokI
ltS0-bgt
300
Ligase T4
300
15
FokI
300
ltS1-tgt
Ligase S1-D

• Example of the computation of a Benenson
  automaton for input ab.
• The numbers in the boxes indicate the lengths of
  the corresponding double-stranded DNA sequences.

300
161
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Programmable and autonomous biomoleculer computer
Contd

• To start the computation and run autonomously,
  the hardware, software and input are mixed till
  (possible) termination.
• The resultant output will be detected and
  reported by gel electrophoresis.
• In the experiment, the automaton processes the
  encoding for the input string ab as shown.

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Programmable and autonomous biomoleculer computer
Contd

• To cleave the input encoding the symbols abt, the
  FokI enzyme recognizes and exposes the 4-mer
  sticky-end 5' -GGCT -3'.
• It represents the state-symbol pair S0a, and has
  been detected by the transition rule T1 of the
  automaton i.e. S0a -? S0 .
• The rule detects this state-symbol, binds
  exactly to the cleaved input molecule and forms a
  fully double-stranded DNA molecule with the help
  of the enzyme ligase.

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Programmable and autonomous biomoleculer computer
Contd

• The next cleaving of FokI will expose a suffix of
  the encoding of the next input symbol b, which is
  interpreted as S0b.
• Its sticky-end fits the transition rule T4, that
  encodes the automaton rule S0b S1.
• Thus, the combination of the current DNA strand
  with T4 and the enzyme ligase leads to another
  fully double-stranded DNA strand.

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Programmable and autonomous biomoleculer computer
Contd

• Finally FokI exposes the overhang 5-TGTC-3' which
  is a suffix of the terminator, and interpreted as
  S1t.
• The overhang is complementary to the sticky-end
  3-ACAG-5' of the detector molecule S1-D, which
  means S1 being the last state of the computation.
  
• The state S1 is not final/ accepting state, and
  hence the input ab is not accepted by this
  automaton.

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Programmable and autonomous biomoleculer computer
Contd

• To observe and verify the independent parallel
  computation, the same program was run on a
  mixture of two different inputs and the results
  were found as expected.
• Computation on a non-deterministic automaton was
  also tested.
• Only computations on input aabb reached the
  accepting state S0, some computations on this
  input reached state S1 and some were suspended
  thus illustrating non -deterministic choices, as
  was expected.

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An autonomous molecular computer for logical
control of gene expression Shapiro and
Benenson, 2004
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An autonomous molecular computer for logical
control of gene expression

• The molecular autonomous programmable computers
  have been described which take biological
  molecules as input and biologically active
  molecules as outputs.
• It is a system for logical control of
  biological processes.

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An autonomous molecular computer for logical
control of gene expression Contd

• The autonomous biomolecular computer (at least in
  vitro), logically analyses messenger RNA species
  and their levels.
• It contains
• A stochastic molecular automaton as a computation
  module
• An input module by which mRNA levels regulate
  software molecule concentration (automaton
  transition probabilities) and
• An output module that releases a short
  single-stranded DNA molecule.
• All the three modules are programmable.

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An autonomous molecular computer for logical
control of gene expression Contd

• This computer operates at a concentration of
  almost trillion computers per micro litre and
  produces a molecule capable of affecting levels
  of gene expression.

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An autonomous molecular computer for logical
control of gene expression Contd

• To prove its application in vivo, the computer
  was programmed to identify and analyse mRNA of
  disease-related genes with models of small-cell
  lung cancer and prostate cancer, and to produce a
  single-stranded DNA molecule.

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A DNA and restriction enzyme Implementation of
Turing Machines Paul Rothemund, 1995
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A DNA and restriction enzyme Implementation of
Turing Machines

• Many restriction enzymes cut the double stranded
  DNA such that single stranded DNA is left
  over-hanging at different positions.
• If the terminal overhangs are complementary they
  may be rejoined.
• Encoding for a transition table of a Turing
  machine has been proposed in DNA
  oligonucleotides, having a Turing tape, head
  position and state.

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A DNA and restriction enzyme Implementation of
Turing Machines Contd

• Transitions have been shown using restriction
  enzyme chemistry.
• By repeating 6 distinct chemical steps, a Turing
  machine has been simulated.
• The transition table which is the machine part of
  the Turing machine has been taken as a guide
  towards DNA implementation of TM in this paper.

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A DNA and restriction enzyme Implementation of
Turing Machines Contd

• The concept of cutting frames provided by class
  IIS restriction enzymes have been used to propose
  encoding of a TM with DNA chemistry.
• It is to be remembered that this is the only
  theoretical work available so far, rest all are
  the experiments.

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Conclusion

• Implementation of Biomolecular Turing machines
  and automata has been discussed using different
  research works.
• These machines have similar concepts of input,
  processing units and output like electronic
  computers.
• Although much ahead to go, current work has
  proved the existence of programmable and
  autonomous biomolecular computers.

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References

• Ehud Shapiro and Yaakov Benenson, Bringing DNA
  Computers to Life, 2006 Scientific American,
  inc.
• Yaakov Benenson, Rivka Adar, Tamar Paz-Elizur,
  Zvi Livneh and Ehud Shapiro, DNA molecule
  provides a computing machine with both data and
  fuel, PNAS, Jan-2003.
• Rivka Adar,Yaakov Benenson, Gregory Linshiz, Amit
  Rosner, Naftali Tishby, and Ehud Shapiro,
  Stochastic Computing with biomolecular
  automata, PNAS July - 2004 vol. 101 no. 27.
• Yaakov Benenson, Binyamin Gil, Uri BenDor, Rivka
  Adar Ehud Shapiro, An autonomous molecular
  computer for logical control of gene expression,
  nature April-2004.
• Yaakov Benenson, Tamar Paz-Elizur, Rivka Adar,
  Ehud Keinan, Zvi Livneh Ehud Shapiro,
  Programmable and autonomous computing machine
  made of Biomolecules, nature Nov-2001.
• Paul Rothemund, A DNA and restriction enzyme
  Implementation of Turing Machines , DNA Based
  Computers Proceedings of a Dimacs Workshop April
  4, 1995 Princeton University.

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Questions