Bio-molecular computing of finite-state automata Yasubumi Sakakibara Biosciences and Informatics...
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Transcript of Bio-molecular computing of finite-state automata Yasubumi Sakakibara Biosciences and Informatics...
Bio-molecular computing of finite-state automata
Yasubumi SakakibaraBiosciences and Informatics
Keio UniversityJapan
9th International Colloquium on Grammatical Inference (ICGI 2008), 2008
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
ATATCCCCCCCCTTTT
GGGGGGGG
DNA strands
CGCGCGCG
Image of DNA Computer
Test Tube
ATATCCCC
CCCCTTTTGGGGGGGG
Hybridization:
CGCGCGCG
Image of DNA Computer
Test Tube
ATATCCCCCCCCTTTT
GGGG GGGG
Hybridization:
Self-Assembly
CGCGCGCG
Leonard Adleman’s seminal work
(Science 266, 1994)
Solved an instance of directed Hamiltonian path problem solely by manipulating DNA sequences
ハミルトン経路問題( HPP)
60
13
2
4
5
Directed Hamiltonian Path Problem (HPP)
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
Advantage of DNA computer:– microscopic DNA molecule offers massively parallel
computation and huge information storage– potential application to molecular biology and medical
research
input output
biological operations
Automaton in silico, in vitro, in vivo
in silico computer in vitro computer
Finite Automata
PushdownAutomata
Linear Bounded Automaton
Turing machine
in vivo computer
Finite Automata Finite Automata
low
(computation pow
er
) high
q0 q1
C
G q4q3
q2 state
transition function
input symbol
q3 q4G
initial state
final state
TA
C
Finite-state Automaton: Example
= { A, C, G, T } (for DNA sequences)
Finite-state Automaton (FA): Definition
Formal Definition of (deterministic) Finite-state Automaton:
states finalof set
state initial
to input on fromn transitiostate
functionn transitiostate
(alphabet) symbols input of set finite
states of set finite
:
:
:
),(
:
:},,{
:},,{
),,,,(
0
1
1
0
QF
q
qqqaq
aa
qqQ
FqQM
jiji a
M
N
q0 q1
Aq2
Tq4
G
q3
CC
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:
• State transition from state i to state j with symbol a :
timestimes1times1
)()()( 21
lmxexexe
kk
TTTTTTTTTTTT
)'5( )( )'3(times1times
jkiae AAAAA
ssDNA:
complementary ssDNA:
(5’) (3’)
‘0’ 5’- CCC -3’
① ssDNA subsequence encoding input symbol:
② Encode input string by joining into ssDNA sequence
DNA sequence design: input symbol
(Ex)
“010”(Ex)
00 1
‘1’ 5’- GGG -3’state
(2 states)5’- TTT -3’
5’- TCCCTTTGGGTTTCCCT -3’
DNA sequence design: transition function
x y0 : AGGGA
Example:
①
x x0 : AGGGAA②
x y1 : ACCCA③
x x1 : ACCCAA④
y y0 : AAGGGA⑤
y x0 : AAGGGAA⑥
y y1 : AACCCA⑦
y x1 : AACCCAA⑧
8 transition rules for two-states FA
x y
0
0
1
0
11
0
1
#1 #2
y y0 : AAGGGA
x x0 : AGGGAA
x y1 : ACCCAy x : AACCCAA
1
TCCCTTTGGGTTTCCCT
Computation process using hybridization:Accepting case
Input string : 010
AGGGAAACCCAAAGGGAAccept
x y
1
1
0
0
Input string : 011
y y0 : AAGGGA
x x0 : AGGGAA
x y1 : ACCCAy x : AACCCAA
1
Computation process using hybridization:Rejecting case
x y
1
1
0
0
AGGGAAACCCAAACCCAATCCCTTTGGGTTTGGGT Reject
Input string : 011
y y0 : AAGGGA
x x0 : AGGGAA
x y1 : ACCCAy x : AACCCAA
1
TCCCTTTGGGTTTGGGT
x y
1
1
0
0
ACCCAAGGGAAACCCAReject
Computation process using hybridization:Rejecting case
Ligase
YYYYYYYYYYYY
detection, purification sequence:XXXXXX-
TTCCCTTTGGGTTTCCCT
input sequence:
Experimental protocol for executing FA in vitro(Kuramochi & Sakakibara, DNA11, 2005)
ACCCAA
AAGGGA
transition function:
AACCCAACCCA
AAGGGAA
Protocol of in vitro automaton
Hybridizationaccept
Ligation
Purification by beads
PCR
reject
PCR sequence
purification sequence
input string
Input symbol ‘0’ GCGTGTACGATGCAG
Input symbol ‘1’ GACGTTGGATGTGGG
state AAGCAGTTTT
purification probe CTGGTTGCTTGTCCC
detection probe CCCTGTTCGTTGGTC
PCR primer CCGACTTCGTACGAGATTAG
concrete ssDNA sequences:
DNA sequences designed with TM control
Experimental result: 2-states FA
0
input strings:
(a) 1101 reject
(b) 1110 reject
(c) 1010 accept
1
(a) (b) (c)
acceptreject reject
190mer
gel-electrophoresis:
finite-automaton:
input strings:
(a) 1101 reject
(b) 1110 accept
(c) 1010 accept
Experimental result: 4-states FA
0
0
1
1 1
(a) (b) (c)
190mer
acceptacceptreject
gel-electrophoresis:
finite-automaton:
Experimental result: from 2-states to 6-states FA
1
1 1
1
1
1
1
1
1
1 1
1
1 1
1
1
11
1
1
input string:
111111
finite-automata:
240mer
2 (accept)
3 (accept)
4 (reject)5 (reject)
6 (accept)
Experimental result: from 2-states to 6-states FA
Input string: 111111 (six ‘1’s)
gel-electrophoresis:
Development of in vivo computerbased on E.coli
Bacteria computer
Protein synthesis (Translation) system Molecular machine to synthesize proteins
• Ribosomes, • tRNAs, • several translation factors
mRNA
Ribosome
tRNA
Translation process to synthesize proteins
DNA-- AUG CCG CAA AUC ACU CUA UGG CAG CGU CCA --
mRNA
transcription
-- AUG CCG CAA AUC ACU CUG UGG CAG CGU UAG --
Met Pro GlnIle
Thr
translations
GAC
Leu
ACC
Trp
Initiation codon stop codon3-base codons
amino acid sequence
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)
AGC CGUUCG
Ser
UCCA
Xaa
mRNAAGGU
4-base codon
4-base anticodon
nonnatural amino acid
tRNA
5-base codon, 6-base, …
Implementing FA: example
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
Parity check 1
1s0 s1
Implementing FA: example
Input symbol ‘1’: AGGU State: A
‘11’ = AGGUAAGGUAAAUAA - reporter gene
‘111’ = AGGUAAGGUAAGGUAAAUAA -reporter gene
1 1
encoding states
stop codon
1 1 1
1
1s0 s1
Encode input string into mRNA:
Implementing FA: example
1
1s0 s1
Encode state transitions into tRNA with anticodons
δ(s0, 1) = s1
+
Encode state-transition function:
δ(s1, 1) = s0
4-base anticodon tRNA
3-base anticodon tRNAs
UCCA
Ser
UUC
Lys Val
CAU
Computation process : accepting case(even number of ‘1’)
5’ - AGGUAAGGUAAAUAAC - reporter gene 3’
mRNAStop codon
1
1
Ser
δ(s0, 1) = s0 δ(s1, 1) = s0
Input string: ’11’
UCCA
Ser
+
UUC
Lys Val
CAU
UCCA
Ser
s1s0
Computation process : accepting case(even number of ‘1’)
5’ - AGGUAAGGUAAAUAAC - reporter gene 3’
mRNAStop codon
1
1s0
Ser Lys
δ(s0, 1) = s0 δ(s1, 1) = s0
Input string: ’11’
UCCA
Ser
+
UUC
Lys Val
CAU
UUC
Lys
s1
Computation process : accepting case(even number of ‘1’)
5’ - AGGUAAGGUAAAUAAC - reporter gene 3’
mRNAStop codon
1
1
Ser Lys
δ(s0, 1) = s0 δ(s1, 1) = s0
Input string: ’11’
UCCA
Ser
+
UUC
Lys Val
CAU
s0 s1
CAU
Val
Val
Computation process : accepting case(even number of ‘1’)
5’ - AGGUAAGGUAAAUAAC - reporter gene 3’
mRNAStop codon
1
1
Ser Lys
δ(s0, 1) = s0 δ(s1, 1) = s0
Input string: ’11’
UCCA
Ser
+
UUC
Lys Val
CAU
s0 s1
Val Asn
UUA
Asn
Computation process : accepting case(even number of ‘1’)
5’ - AGGUAAGGUAAAUAAC - reporter gene 3’
mRNAStop codon
1
1
Ser Lys
δ(s0, 1) = s0 δ(s1, 1) = s0
Input string: ’11’
UCCA
Ser
+
UUC
Lys Val
CAU
s0 s1
Val Asn
UUG
LeuLeu
Translation continue
Computation process : rejecting case(odd number of ‘1’)
5’ - AGGUAAGGUAAGGUAAAUAAC - reporter gene 3’
mRNAStop codon
Input string: ’111’
δ(s0, 1) = s0 δ(s1, 1) = s0
UCCA
Ser
+
UUC
Lys Val
CAUSer
UCCA
Ser
1
1s1s0
Computation process : rejecting case(odd number of ‘1’)
5’ - AGGUAAGGUAAGGUAAAUAAC - reporter gene 3’
mRNAStop codon
Input string: ’111’
δ(s0, 1) = s0 δ(s1, 1) = s0
UCCA
Ser
+
UUC
Lys Val
CAU
1
1s0
Ser Lys
UUC
Lys
s1
Computation process : rejecting case(odd number of ‘1’)
5’ - AGGUAAGGUAAGGUAAAUAAC - reporter gene 3’
mRNAStop codon
Input string: ’111’
δ(s0, 1) = s0 δ(s1, 1) = s0
UCCA
Ser
+
UUC
Lys Val
CAU
1
1
Ser Lys
s0 s1
CAU
Val
Val
Computation process : rejecting case(odd number of ‘1’)
5’ - AGGUAAGGUAAGGUAAAUAAC - reporter gene 3’
mRNAStop codon
Input string: ’111’
δ(s0, 1) = s0 δ(s1, 1) = s0
UCCA
Ser
+
UUC
Lys Val
CAU
UCCA
Ser
Ser Lys Val Ser
1
1s0 s1
Computation process : rejecting case(odd number of ‘1’)
5’ - AGGUAAGGUAAGGUAAAUAAC - reporter gene 3’
mRNAStop codon
Input string: ’111’
δ(s0, 1) = s0 δ(s1, 1) = s0
UCCA
Ser
+
UUC
Lys Val
CAU
1
1s1s0
UUU
Phe
Ser Lys Val Ser
Computation process : rejecting case(odd number of ‘1’)
5’ - AGGUAAGGUAAGGUAAAUAAC - reporter gene 3’
mRNAStop codon
Input string: ’111’
δ(s0, 1) = s0 δ(s1, 1) = s0
UCCA
Ser
+
UUC
Lys Val
CAU
1
1s1s0
UUU
Phe
Ser Lys Val Ser
Designing Plasmid for input string
Reporter gene: lacZ
Designing Plasmid for 4-base UCCU anticodon tRNA
An in vivo computer based on E.coliplasmid encoding input string
plasmid encoding Ser tRNA reading AGGU
E. coli
LacZ expression
colony exhibits a blue color = accept
incubation= computation
LacZ no expression
transformation
colony exhibits no color = reject
Experimental result
(+)(-)
(-)
(-)
(-)
(-)
(+)
(-)
(+)
(-)
(-)
(-)
theoretical sign
n = 1”1”
n = 2”11”
n = 3”111”
n = 4”1111”
n = 5”11111”
n = 6”1111111”
(UCCU)
with tRNA
(UCCU)
without tRNA
Programmable and autonomous in vivo computer
plasmid encoding input string
Programmable:choosing plasmid encoding tRNAs
E. coli
Autonomous:computation is executed by living E.coli
transformation. . .A B Z
Build our Wet Laboratory from Zero
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.