Molecular State Machines

Masami Hagiya

Finite State Machines

• Are the simplest formal computing device

• Have a finite number of states

• Change their state autonomously or according to inputs

• May produce outputs

• Are the first step towards general-purpose computers

• Have many kinds of applications– Switch– Memory (both holding contents and addressing)

Molecular (DNA) State Machines

• Terminal-sequence machines– The terminal sequence encodes the state.– Our whiplash machine

• The machine gets longer as it changes the state.

– Shapiro’s automaton• The machine gets shorter as it changes the state.

• Conformational machines– The state is encoded as a structure.– Yurk’s molecular tweezers

– Seeman’s PX-JX2 Switch

– Our hairpin-based machine…

B AC

B

: stopper sequence

1)B

B AC

B

A2) B

A

Whiplash PCR (WPCR)

Whiplash PCR (WPCR)

B A C B

3)

B A

C

B A C B

4)B

A

Polymerization Stop

B A C B

B A

Back-hybridization

B A C B

B

A

B A C

BB A

Competing Alternative Hairpin Forms

・ 8 M urea 8% PAGE

Temperature optimization for WPCR

incubated 62.2 69.9 78.0 86.1 92.2 (℃)not 59.8 65.9 74.0 82.1 89.8

in 1X Pfx buffer (the composition unknown) 1 mM MgSO4

0.2 mM dATP, dCTP, dGTP 1.5 units Platinum Pfx DNA polymerase

Thermal schedule 94 for 1 min.℃

　 ↓ x for 5 min.℃ x =59.8 ~ 92.2

Komiya, et al.

・ 12 ％ PAGE

65

80

95110125140

50

155

( bp )

Successful implementation of transitions

Komiya, et al.

Whiplash Machines

• The machine changes its state according to its own transition table.

• Various kinds of information can be encoded as a transition table.– Inputs to the machine can be a part of the table.

• Multiple-data Multiple-program

Shapiro’s DNA AutomatonIIS-type restrictionRestriction cite Spacer

<S,a><S,a>

a’ Rest of input

Rest of input

a’ Rest of input

<S’,a’>

S,a → S’Transition molecule

The input sequence for a’ contains <S’,a’> for each state S’.The transition molecule cuts the input at the right place by the spacer.

Shapiro’s DNA Automaton

• Nature 2001

• 2 input symbols, 2 states

• FokI

a=CTGGCT b=CGCAGC

5’-p…22…GGATGTAC3’-GGT…22…CCTACATGCCGAp

5’-p…22…GGATGACGAC3’-GGT…22…CCTACTGCTGCCGAp

S0,a→S0

S0,a→S1

Yurke: DNA Tweezers

Seeman: PX-JX2 Switch

Multi-state Molecular Machine

input1

input2

input3

2

1

2

3

1

3

3 3

１

2

……

……

……Our goals:Successive state changeInput order sensitive

Hairpin-based Machine

Hairpin_template Oligomer

20

7

2020

(67 bp + 3’ FITC)

Oligomer1Oligomer2Oligomer3Oligomer4

20 + 20 = 40bp15 + 20 = 35bp10 + 20 = 30bp 5 + 20 = 25bp

Oliogomer : ヘアピン構造を開くために用いるｓｓ DNA

A B C D E10 % PAGEA : Hairpin_templateB : Hairpin_template + oligomer1C : Hairpin_template + oligomer2D : Hairpin_template + oligomer3E : Hairpin_template + oligomer4

シングルヘアピンの状態遷移確認実験

B ではシングルヘアピン構造にオリゴマーが結合し，ヘアピン構造が開いて状態遷移している．そのためヘアピン構造を示すバンドが減少し，新たにヘアピン構造が開いた状態のバンドが現れている．

分子の構造変化経路

ΔG1

ΔG2

二次構造

ΔG1 の最小化⇒構造変化の高速化

妥当な変化経路の予測が必要

局所最適最短経路

大域最適最短経路

大域最適経路

自由エネルギー

DNA へのアゾベンゼンの導入

DNA に挿入されたアゾベンゼンの状態により， hybridization の安定度が変化する。 (Asanuma et al., 1999)

300 nm<<400 nm

400 nm<

二重鎖の形成と解離の光制御に成功

trans

二重鎖が形成

cis

二重鎖が解離

Lights as Inputs (still a dream)