Download 1 - ICGI 2008

9th International Colloquium on Grammatical Inference
(ICGI 2008), 2008
Bio-molecular computing of finite-state
automata
Yasubumi Sakakibara
Biosciences and Informatics
Keio University
Japan
What is DNA computer?

Computer in vitro or in vivo
• Computational devise: DNA strands
• Adenine, Cytosine, Guanine, Thymine
• Watson-Crick complement (bonding)
A – T, C – G
• Biological operations to do Computation:
•
•
•
•
Annealing
Amplifying
Ligation
…
• DNA sequences are used to encode information
while enzymes can be employed to simulate
simple computations
Image of DNA Computer
Test Tube
DNA
strands
Image of DNA Computer
Test Tube
Hybridization:
Image of DNA Computer
Test Tube
Self-Assembly
Hybridization:
Leonard Adleman’s seminal work
(Science 266, 1994)
Solved an instance of
directed Hamiltonian
path problem solely by
manipulating DNA
sequences
Directed Hamiltonian
Path Problem (HPP)
ハミルトン経路問題（HPP)
4
3
1
0
6
2
5
List of molecular biological operations








Synthesis of a desired DNA strand (sequence)
Separation of DNA strands by length
using gel-electrophoresis
Merging : pour two test tubes into one to do union
Extraction : extract DNA strands containing a given pattern
as a subsequence
Melting/Annealing : break apart/bond together two single
DNA strands with complementary sequences
Amplifying : make copies of DNA strands by using
Polymerase Chain Reaction (PCR)
Cutting : cut DNA strands by using restriction enzymes
Ligation : concatenate DNA strands by using ligase
Computational process of DNA computer
•
Computational process of DNA computer:
a sequence of test tubes
biological
operations
input

output
Advantage of DNA computer:
– microscopic DNA molecule offers massively parallel
computation and huge information storage
– potential application to molecular biology and medical
research
Automaton in silico, in vitro, in vivo
in silico computer
low computation power high
（
）
in vitro computer
in vivo computer
Turing machine
Linear Bounded
Automaton
Pushdown
Automata
Finite Automata
Finite Automata
Finite Automata
Finite-state Automaton: Example
q2
input
symbol
q0
A
final state
C
C
q1
state
T
G
q3
initial
state
transition
function
q3
S = { A, C, G, T }
q4
(for DNA sequences)
G
q4
Finite-state Automaton (FA): Definition
Formal Definition of (deterministic) Finite-state Automaton:
M  (Q, S,  , q0 , F )
 Q  {q1 ,, q N } : finite
set of states
 S  {a1 ,, aM } : finite
set of inputsymbols (alphabet)
  : state transitio
n function
 (qi , a)  q j :state transitio
n fromqi on inputa toq j
 q0 : initial
state
 F  Q : set of final
states
q
3
C
q
A
0
q
C
T
1
q
G
2
q
4
Implementation of Finite Automata in vitro
Length-encoding method to implement FA
(Yokomori, Sakakibara, & Kobayashi, 2002)
•
Finite automaton with k states (from #1 to #k)
•
Encode input string x1x2…xm into ssDNA:
Te( x 2 )TTT
T e( x m )TT

T (3’)
ssDNA: (5’) Te( x1 )TTT









l times
k 1 times
k 1 times
•
State transition from state i to state j with symbol a :
complementary (3' ) A  A e(a) AA  A (5' )




ssDNA:
i times
k  j 1 times
DNA sequence design: input symbol
① ssDNA subsequence encoding input symbol:
(Ex)
‘0’
‘1’
state
5’- CCC -3’
5’- GGG -3’
5’- TTT -3’
(2 states)
② Encode input string by joining into ssDNA
sequence
(Ex) “010”
5’- TCCCTTTGGGTTTCCCT -3’
0
1
0
DNA sequence design:
transition function
Example:
8 transition rules for
two-states FA
#1
#2
0
1
x
1
1
1
y
0
0
0
①
x
0
y : AGGGA
⑤y
0
y : AAGGGA
②
x
0
x : AGGGAA
⑥y
0
x : AAGGGAA
③
x
1
y : ACCCA
⑦y
1
y : AACCCA
x
1
x : ACCCAA
⑧y
1
x : AACCCAA
④
Computation process using hybridization:
Accepting case
x
y
1
x
y
0
1
0
y : ACCCA
x : AACCCAA
1
0
x
x : AGGGAA
y : AAGGGA
y
1
0
Input string : 010
TCCCTTTGGGTTTCCCT
AGGGAAACCCAAAGGGA
Accept
Computation process using hybridization:
Rejecting case
x
y
1
x
y
0
1
0
y : ACCCA
x : AACCCAA
x : AGGGAA
y : AAGGGA
1
0
x
y
1
0
Input string : 011
TCCCTTTGGGTTTGGGT Reject
AGGGAAACCCAAACCCAA
Computation process using hybridization:
Rejecting case
x
y
1
x
y
0
1
0
y : ACCCA
x : AACCCAA
x : AGGGAA
y : AAGGGA
1
0
x
y
1
Input string : 011
TCCCTTTGGGTTTGGGT Reject
AGGGAAACCCA ACCCA
0
Experimental protocol for executing FA in vitro
(Kuramochi & Sakakibara, DNA11, 2005)
transition function:
AAGGGA
AAGGGAA
ACCCAA
ACCCA
AACCCA
detection,
purification
sequence:
XXXXXX－
YYYYYYYYYYYY
input sequence:
TTCCCTTTGGGTTTCCCT
Ligase
Protocol of in vitro automaton
accept
Hybridization
input string
PCR
sequence
purification
sequence
Ligation
Purification
by beads
PCR
reject
DNA sequences designed with TM control
concrete ssDNA sequences:
Input symbol ‘0’
GCGTGTACGATGCAG
Input symbol ‘1’
GACGTTGGATGTGGG
state
AAGCAGTTTT
purification probe
CTGGTTGCTTGTCCC
detection probe
CCCTGTTCGTTGGTC
ＰＣＲ primer
CCGACTTCGTACGAGATTAG
Experimental result: 2-states FA
input strings:
finite-automaton:
(a) 1101 reject
1
(b) 1110 reject
0
(c) 1010 accept
gel-electrophoresis:
reject
reject
accept
(a)
(b)
(c)
190mer
Experimental result: 4-states FA
finite-automaton:
input strings:
0
(a) 1101 reject
1
1
(b) 1110 accept
1
0
(c) 1010 accept
gel-electrophoresis:
reject
accept
accept
190mer
(a)
(b)
(c)
Experimental result: from 2-states to 6-states FA
finite-automata:
input string:
111111
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
Experimental result: from 2-states to 6-states FA
Input string: 111111 (six ‘1’s)
gel-electrophoresis:
240mer
２
３
４
５
６
(accept)
(accept)
(reject)
(reject)
(accept)
Development of in vivo computer
based on E.coli
Bacteria computer
Protein synthesis (Translation) system

Molecular machine to synthesize proteins
• Ribosomes,
• tRNAs,
• several translation factors
Ribosome
tRNA
mRNA
Translation process to synthesize proteins
-- AUG CCG CAA AUC ACU CUA UGG CAG CGU CCA --
DNA
transcription
mRNA
translations
amino acid sequence
Met Pro Gln
Ile
Trp
Thr
Leu
ACC
GAC
-- AUG CCG CAA AUC ACU CUG UGG CAG CGU UAG --
Initiation codon
3-base codons
stop codon
Methods for implementing FA in vivo
(Nakagawa, Sakamoto, & Sakakibara, DNA11, 2005)




Use protein-synthesis mechanism of E.coli
+ 4-base codon technique
Input string
→ encoded to mRNA
State-transition function
→ encoded to 3, 4-base anticodon
Translation of mRNA = Computation (accepting)
process of FA
in vitro (low translation efficiency) → in vivo
(Sakakibara & Hohsaka, DNA 9, 2003)
Four-base codon techniques
(Hohsaka et al, 2001)
Xaa nonnatural amino acid
Ser
tRNA
UCCA 4-base anticodon
UCG
AGC AGGU CGU
4-base codon
mRNA
5-base codon, 6-base, …
Implementing FA: example
1
s0
s1
Parity check
1
State = {s0, s1}
Input symbol = {1}
State-transition function:
δ(s0,1) = s1, δ(s1,1) = s0
Initial & Final state: s0
Number of input symbols ‘1’
Even → Accept
Odd → Reject
Implementing FA: example
1
Encode input string
into mRNA:
s0
s1
1
Input symbol ‘1’: AGGU
State: A
‘11’ = AGGUAAGGUAAAUAA－reporter gene
1
1
encoding states
stop
codon
‘111’ = AGGUAAGGUAAGGUAAAUAA－reporter gene
1
1
1
Implementing FA: example
1
Encode state transitions
into tRNA with anticodons
s0
s1
1
Encode state-transition function:
Ser
δ(s0, 1) = s1
4-base anticodon tRNA
UCCA
Lys
δ(s1, 1) = s0
Val
3-base anticodon
tRNAs
+
UUC
CAU
Computation process : accepting case
(even number of ‘1’)
δ(s0, 1) = s0
1
s0
1
s1
Ser
δ(s1, 1) = s0
Lys
Val
+
Ser
Input string:
’11’
mRNA
UCCA
UUC
Ser
UCCA
5’ － AGGUAAGGUAAAUAAC － reporter gene
Stop codon
3’
CAU
Computation process : accepting case
(even number of ‘1’)
δ(s0, 1) = s0
1
s0
1
s1
Ser
δ(s1, 1) = s0
Lys
Val
+
Ser
Input string:
’11’
mRNA
Lys
UCCA
UUC
Lys
UUC
5’ － AGGUAAGGUAAAUAAC － reporter gene
Stop codon
3’
CAU
Computation process : accepting case
(even number of ‘1’)
δ(s0, 1) = s0
1
s0
1
s1
Ser
δ(s1, 1) = s0
Lys
Val
+
Ser
Input string:
’11’
mRNA
Lys Val
UCCA
UUC
Val
CAU
5’ － AGGUAAGGUAAAUAAC － reporter gene
Stop codon
3’
CAU
Computation process : accepting case
(even number of ‘1’)
δ(s0, 1) = s0
1
s0
s1
1
Ser
δ(s1, 1) = s0
Lys
Val
+
Ser
Input string:
’11’
mRNA
Lys Val
Asn
UCCA
UUC
Asn
UUA
5’ － AGGUAAGGUAAAUAAC － reporter gene
Stop codon
3’
CAU
Computation process : accepting case
(even number of ‘1’)
δ(s0, 1) = s0
1
s0
1
s1
Ser
δ(s1, 1) = s0
Lys
Val
+
Ser
Input string:
’11’
Lys Val
Asn Leu
Leu
UCCA
UUC
CAU
Translation continue
mRNA
UUG
5’ － AGGUAAGGUAAAUAAC － reporter gene
Stop codon
3’
Computation process : rejecting case
(odd number of ‘1’)
δ(s0, 1) = s0
1
s0
1
s1
Ser
δ(s1, 1) = s0
Lys
Val
+
Ser
Input string:
’111’
mRNA
UCCA
UUC
CAU
Ser
UCCA
5’ － AGGUAAGGUAAGGUAAAUAAC － reporter gene
Stop codon
3’
Computation process : rejecting case
(odd number of ‘1’)
δ(s0, 1) = s0
1
s0
1
s1
Ser
δ(s1, 1) = s0
Lys
Val
+
Ser
Input string:
’111’
mRNA
Lys
UCCA
UUC
CAU
Lys
UUC
5’ － AGGUAAGGUAAGGUAAAUAAC － reporter gene
Stop codon
3’
Computation process : rejecting case
(odd number of ‘1’)
δ(s0, 1) = s0
1
s0
1
s1
Ser
δ(s1, 1) = s0
Lys
Val
+
Ser
Input string:
’111’
mRNA
Lys Val
UCCA
UUC
CAU
Val
CAU
5’ － AGGUAAGGUAAGGUAAAUAAC － reporter gene
Stop codon
3’
Computation process : rejecting case
(odd number of ‘1’)
δ(s0, 1) = s0
1
s0
s1
1
Ser
δ(s1, 1) = s0
Lys
Val
+
Ser
Input string:
’111’
mRNA
Lys Val
Ser
UCCA
UUC
CAU
Ser
UCCA
5’ － AGGUAAGGUAAGGUAAAUAAC － reporter gene
Stop codon
3’
Computation process : rejecting case
(odd number of ‘1’)
δ(s0, 1) = s0
1
s0
s1
1
Ser
δ(s1, 1) = s0
Lys
Val
+
Ser
Input string:
’111’
mRNA
Lys Val
UCCA
Ser
UUC
CAU
Phe
UUU
5’ － AGGUAAGGUAAGGUAAAUAAC － reporter gene
Stop codon
3’
Computation process : rejecting case
(odd number of ‘1’)
δ(s0, 1) = s0
1
s0
s1
1
Ser
δ(s1, 1) = s0
Lys
Val
+
Ser
Input string:
’111’
mRNA
Lys Val
UCCA
Ser
UUC
CAU
Phe
UUU
5’ － AGGUAAGGUAAGGUAAAUAAC － reporter gene
Stop codon
3’
Designing Plasmid for input string
Reporter gene: lacZ
Designing Plasmid for 4-base UCCU anticodon tRNA
An in vivo computer based on E.coli
plasmid encoding
input string
plasmid encoding Ser tRNA
reading AGGU
transformation
E. coli
LacZ expression
colony exhibits a blue
color = accept
incubation
= computation
LacZ no expression
colony exhibits no
color = reject
Experimental result
n=1
”1”
n=2
n=3
”11”
”111”
with
tRNA
(UCCU) (－)
without
tRNA (－)
(UCCU)
(+)
(－)
(－)
(－)
n=4
n=5
n=6
”1111”
”11111”
”1111111”
theoretical (+)
sign
(－)
(+)
(－)
(－)
(－)
Programmable and autonomous
in vivo computer
plasmid encoding
input string
Programmable:
choosing plasmid encoding tRNAs
transformation
A
B
...
E. coli
Autonomous:
computation is executed by living E.coli
Z
Build our Wet Laboratory from Zero
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Cloning
Recombinant DNA
Gel-electrophoresis
Transformation by
electroporation
Competent cell
Operations on E.coli
Design plasmids
Protein synthesis in vitro
and in vivo
RT-PCR
P1 level
References:

H.Nakagawa, K.Sakamoto, and Y.Sakakibara : Development of an in
vivo computer based on Escherichia coli, Proceedings of 11th
International Meeting on DNA Based Computers, 68-77, 2005

J.Kuramochi and Y.Sakakibara : Intensive in vitro experiments of
implementing and executing finite automata in test tube, Proceedings
of 11th International Meeting on DNA Based Computers, 59-67, 2005.

Y.Sakakibara and T.Hohsaka : In Vitro Translation-based Computations,
Proceedings of 9th International Meeting on DNA Based Computers,
175-179, 2003.

T.Yokomori, Y.Sakakibara, and S.Kobayashi : A Magic Pot : Self-
assembly computation revisited, Formal and Natural Computing,
Lecture Notes in Computer Science 2300, Springer-Verlag, 418--429,
2002.