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Molecular Computing: An Overview - SNU Computing: An Overview. Byoung-Tak Zhang. ... molecular...
91
Molecular Computing: Molecular Computing: An Overview An Overview Byoung-Tak Zhang Biointelligence Laboratory School of Computer Science and Engineering, Seoul National University March 13, 2002
Transcript of Molecular Computing: An Overview - SNU Computing: An Overview. Byoung-Tak Zhang. ... molecular...
Mol
ecul
ar C
ompu
ting:
M
olec
ular
Com
putin
g:
An O
verv
iew
An O
verv
iew
Byo
ung-
Tak
Zhan
g
Bio
inte
llige
nce
Labo
rato
rySc
hool
of C
ompu
ter S
cien
ce a
nd E
ngin
eerin
g,Se
oul N
atio
nal U
nive
rsity
Mar
ch 1
3, 2
002
(C) 2
002,
SN
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ioin
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e La
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/2
Out
line
Out
line
Wha
t Is M
olec
ular
Com
putin
g?D
NA
Com
putin
g O
pera
tors
Exam
ples
♦So
lvin
g a
Com
bina
toria
l Pro
blem
♦Th
eore
m P
rovi
ng U
sing
DN
ATh
e D
iffic
ultie
s of D
NA
Com
pute
rD
NA
Com
putin
g A
pplic
atio
nsC
oncl
usio
n In
form
atio
n So
urce
s
(C) 2
002,
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ioin
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e La
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Bioc
ompu
ting
Bioc
ompu
ting
vs. B
ioin
form
atic
svs
. Bio
info
rmat
ics
Bio
info
rmat
ics
BT
BT
ITIT
Bio
com
putin
g
Wha
t Is
Mol
ecul
ar C
ompu
ting?
Wha
t Is
Mol
ecul
ar C
ompu
ting?
The
use
of b
iolo
gica
l mol
ecul
es,
prim
arily
DN
A, D
NA
anal
ogs,
and
RN
A, f
or c
ompu
tatio
n pu
rpos
e.
(C) 2
002,
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ioin
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e La
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/5
DN
A C
ompu
ting
DN
A C
ompu
ting
(C) 2
002,
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ioin
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e La
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/5
DN
A C
ompu
ting
DN
A C
ompu
ting
(C) 2
002,
SN
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ioin
telli
genc
e La
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/5
DN
A C
ompu
ting
DN
A C
ompu
ting
(C) 2
002,
SN
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ioin
telli
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e La
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/5
DN
A C
ompu
ting
DN
A C
ompu
ting
(C) 2
002,
SN
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ioin
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e La
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/5
DN
A C
ompu
ting
DN
A C
ompu
ting
(C) 2
002,
SN
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ioin
telli
genc
e La
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/5
DN
A C
ompu
ting
DN
A C
ompu
ting
(C) 2
002,
SN
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ioin
telli
genc
e La
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/5
DN
A C
ompu
ting
DN
A C
ompu
ting
(C) 2
002,
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ioin
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e La
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/5
DN
A C
ompu
ting
DN
A C
ompu
ting
(C) 2
002,
SN
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ioin
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e La
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DN
A C
ompu
ting
DN
A C
ompu
ting
0110
0110
1010
001
(C) 2
002,
SN
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ioin
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e La
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/5
DN
A C
ompu
ting
DN
A C
ompu
ting
0110
0110
1010
001
(C) 2
002,
SN
U B
ioin
telli
genc
e La
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/5
DN
A C
ompu
ting
DN
A C
ompu
ting
0110
0110
1010
001
ATG
CTC
GA
AG
CT
(C) 2
002,
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ioin
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e La
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A D
iffer
ent A
ppro
ach
A D
iffer
ent A
ppro
ach
Wha
t DN
A c
ompu
ting
is:
♦a
com
plet
ely
new
met
hod
amon
g a
few
oth
ers (
e.g.
, qu
antu
m c
ompu
ting)
of g
ener
al c
ompu
tatio
n al
tern
ativ
e to
ele
ctro
nic/
sem
icon
duct
or te
chno
logy
♦us
es b
ioch
emic
al p
roce
sses
bas
ed o
n D
NA
Wha
t DN
A c
ompu
ting
isn’
t:♦
not t
o co
nfus
e w
ith b
io-c
ompu
ting
whi
ch a
pplie
s bi
olog
ical
law
s (ev
olut
ion,
sele
ctio
n) to
com
pute
r al
gorit
hm d
esig
n.
(C) 2
002,
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e La
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Why
Try
New
Stu
ff ?
Why
Try
New
Stu
ff ?
Will
nee
d a
dram
atic
ally
new
tech
nolo
gy to
ov
erco
me
som
e C
MO
S lim
itatio
ns a
nd o
ffer
new
op
portu
nity
.C
erta
in ty
pes o
f pro
blem
s (le
arni
ng, p
atte
rn
reco
gniti
on, f
ault-
tole
rant
syst
em, l
arge
set s
earc
h al
gorit
hms)
are
intri
nsic
ally
ver
y di
ffic
ult t
o so
lve
even
with
fast
evo
lutio
n of
CM
OS.
Hop
e of
ach
ievi
ng m
assi
ve p
aral
lelis
m.
(C) 2
002,
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ioin
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e La
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Why
Try
DN
A C
ompu
ting?
Why
Try
DN
A C
ompu
ting?
6.02
2 ×
1023
mol
ecul
es /
mol
eof
All
Poss
ibili
ties
♦D
eskt
op: 1
09op
erat
ions
/ se
c♦
Supe
rcom
pute
r: 10
12 o
pera
tions
/ se
c♦
1 µm
olof
DN
A: 1
026 re
actio
ns
: Gib
b’s F
ree
Ener
gy
♦1
Jfo
r 2
×10
19op
erat
ions
: 1 b
it pe
r cub
ic n
anom
eter
-1m
ol
8kca
lG
−=
∆
Mas
sive
ly P
aral
lel S
earc
h
Favo
rabl
e En
erge
tics
Stor
age
Cap
acity
(C) 2
002,
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Why
Try
DN
A C
ompu
ting?
Why
Try
DN
A C
ompu
ting?
The
fast
est s
uper
com
pute
r vs.
DN
A c
ompu
ter
♦10
6op
/sec
vs.
1014
op/s
ec♦
109
op/J
vs.
1019
op/J
(in li
gatio
nst
ep)
♦1b
it pe
r 1012
nm3
vs. 1
bit
per 1
nm
3
(vid
eo ta
pe v
s. m
olec
ules
)
(C) 2
002,
SN
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ioin
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e La
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/10
Know
n C
MO
S lim
itatio
nsKn
own
CM
OS
limita
tions
1999
2002
2005
2008
2011
Sour
ce: T
exas
Inst
rum
ents
and
140
nm
80 n
m
60 n
m
45 n
mpa
ram
eter
s ap
proa
ch
mol
ecul
e si
ze
Gat
e le
ngth
4.0
2.7
1.6-
2.2
1.6-
2.2
0.25
1
4
16
Rel
ativ
e Fa
bC
ost
Inte
r-m
etal
Die
lect
ric K
<1.5
ITR
S IC
Des
ign
Tech
nolo
gy
Wor
king
Gro
up
(C) 2
002,
SN
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ioin
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e La
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/11
Futu
re T
echn
olog
y En
able
rsFu
ture
Tec
hnol
ogy
Enab
lers
Sour
ce: M
otor
ola,
Inc,
200
0N
ow+2
+4+6
+8+1
0+1
2
Full
mot
ion
mob
ile
vide
o/of
fice
Met
al g
ates
, H
i-k/m
etal
ox
ides
, Lo-
k w
ith C
u, S
OI
Perv
asiv
e vo
ice
reco
gniti
on, “
smar
t”tra
nspo
rtatio
n
Ver
tical
/3D
C
MO
S, M
icro
-w
irele
ss n
ets,
Inte
grat
ed o
ptic
s
Smar
t lab
-on-
chip
, pl
astic
/prin
ted
ICs,
self-
asse
mbl
y
Qua
ntum
com
pute
r, m
olec
ular
ele
ctro
nicsB
io-e
lect
ric
com
pute
rs
Wea
rabl
e co
mm
unic
atio
ns,
wire
less
rem
ote
med
icin
e,
‘har
dwar
e ov
er in
tern
et’!
1e6-
1e7
x lo
wer
pow
er
for l
ifetim
e ba
tterie
s
True
neu
ral c
ompu
ting
This
talk
(C) 2
002,
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His
toric
al T
imel
ine
His
toric
al T
imel
ine
Res
earc
h19
50’s
…
R.F
eynm
an’s
pape
r on
sub
mic
rosc
opic
com
pute
rs
1994
L.A
dlem
an so
lves
H
amilt
onia
n pa
th
prob
lem
usi
ng D
NA
.Fi
eld
star
ted
1995
D.B
oneh
pap
er
on b
reak
ing
DE
S w
ith D
NA
Com
mer
cial
1970
’s …
DN
A u
sed
in b
io
appl
icat
ion
1996
Hum
an
Gen
ome
Sequ
ence
d
2000
2000
DN
A c
ompu
ter
arch
itect
ure
?
Aff
ymet
rix
sells
Gen
eChi
pD
NA
ana
lyze
r
2015
Com
mer
cial
co
mpu
ter
?
2005
Luc
ent
build
s DN
A“m
otor
”
(C) 2
002,
SN
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ioin
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e La
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Wha
tW
hat ’’ s
Up
to D
ate
s U
p to
Dat
e
Res
earc
h st
ill in
ver
y ea
rly st
ages
but
pro
mis
e is
big
Firs
t gro
undb
reak
ing
wor
k by
Adl
eman
at U
SC o
nly
6 ye
ars a
goN
o co
mm
erci
aliz
atio
n in
sigh
t with
in ~
10 y
ears
Mai
n w
ork
on se
ttlin
g fo
r a lo
gic
abst
ract
ion
mod
el, w
ays
of u
sing
DN
A to
com
pute
Res
earc
h sp
onso
red
by u
nive
rsiti
es (P
rince
ton,
MIT
, USC
, R
utge
rs, e
tc) a
nd N
EC, L
ucen
t Bel
l Lab
s, Te
lcor
dia,
IBM
One
way
or a
noth
er, D
NA
com
putin
g w
ill h
ave
a si
gnifi
cant
impa
ct
(C) 2
002,
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DN
A C
ompu
ters
vs.
D
NA
Com
pute
rs v
s.
Con
vent
iona
l Com
pute
rsC
onve
ntio
nal C
ompu
ters
elec
troni
c da
ta a
re v
ulne
rabl
ebu
t ca
n be
bac
ked
up e
asily
DN
A is
sens
itive
to c
hem
ical
de
terio
ratio
n
setti
ng u
p on
ly re
quire
skey
boar
d in
put
setti
ng u
p a
prob
lem
may
invo
lve
cons
ider
able
pre
para
tions
smal
ler m
emor
yca
n pr
ovid
e hu
ge m
emor
yin
smal
l sp
ace
can
do su
bsta
ntia
lly fe
wer
ca
n do
bill
ions
of o
pera
tions
fast
at in
divi
dual
ope
ratio
nssl
owat
indi
vidu
al o
pera
tions
oper
atio
nssi
mul
tane
ousl
ysi
mul
tane
ousl
y
Mic
roch
ip-b
ased
com
pute
rsD
NA
-bas
ed c
ompu
ters
(C) 2
002,
SN
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ioin
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e La
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DN
A C
ompu
ting
Take
s Ad
vant
age
DN
A C
ompu
ting
Take
s Ad
vant
age
of
of O
ur a
bilit
y to
pro
duce
mas
sive
num
bers
of D
NA
m
olec
ules
with
spec
ific
prop
ertie
s (si
ze, s
eque
nce)
The
natu
ral p
rocl
ivity
of s
peci
fic D
NA
mol
ecul
es
to c
hem
ical
ly in
tera
ct a
ccor
ding
to d
efin
ed ru
les t
o pr
oduc
e ne
w m
olec
ules
Labo
rato
ry te
chni
ques
that
allo
w th
e is
olat
ion/
iden
tific
atio
n of
pro
duct
mol
ecul
es w
ith
spec
ific
prop
ertie
s♦
PCR
, Lig
atio
n, G
el E
lect
roph
ores
is, e
tc.
DN
A C
ompu
ting
Ope
rato
rsD
NA
Com
putin
g O
pera
tors
(C) 2
002,
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e La
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Basi
c Bu
ildin
g Bl
ocks
Basi
c Bu
ildin
g Bl
ocks
Foun
d in
eve
ry c
ell’s
nuc
leus
, gen
es c
onsi
st o
f tig
ht c
oils
of
DN
A’s
dou
ble
helix
Num
ber o
f gen
es/le
ngth
of D
NA
dep
ends
on
spec
ies
Cel
l
nucl
eus
chro
mos
ome
gene
s
DN
A
(C) 2
002,
SN
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ioin
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e La
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DN
A St
ruct
ure
DN
A St
ruct
ure
Wat
son-
Cric
k co
mpl
emen
t
(C) 2
002,
SN
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ioin
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e La
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/19
DN
A M
emor
y D
NA
Mem
ory
A st
ring
com
pose
d of
a se
ries o
f fou
r typ
es o
f uni
ts
(nuc
leot
ides
), D
NA
may
be
view
ed a
s log
ic m
emor
y or
gat
e.
Nuc
leot
ide
A
GD
NA
bin
ding
has a
com
plem
ent A
ATG
TC
Num
ber S
yste
m (B
ase
4):
Com
plem
ent
Nuc
leot
ide
C
T
proc
ess
ed a
s com
plem
ents
. Exa
mpl
e:Tw
o st
rings
of D
NA
are
bon
ded
by p
aire
d nu
cleo
tides
A-C
an
d C
-G w
hich
may
be
cons
ider
Num
ber T
TAC
AG
(C) 2
002,
SN
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ioin
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e La
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/20
DN
A M
emor
yD
NA
Mem
ory
DN
Am
emor
y st
rand
s
a t
c
g
gt
c
a
t a
g c
a
c
t0
00
a t
c
g
gt
c
a
t a
10
1t
a g
c
c
c g
t
g
a
Writ
ing
: mak
e D
NA
sequ
ence
s
Rea
ding
: hyb
ridiz
atio
n an
d re
adou
t
(C) 2
002,
SN
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ioin
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e La
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DN
A O
pera
tors
DN
A O
pera
tors
The
bio-
lab
tech
nolo
gy.
Hyb
ridiz
atio
nLi
gatio
nPo
lym
eras
e C
hain
Rea
ctio
n (P
CR
)G
el e
lect
roph
ores
isA
ffin
ity se
para
tion
(Bea
d)En
zym
es: r
estri
ctio
n en
zym
e…
(C) 2
002,
SN
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e La
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Hyb
ridiz
atio
n &
Hyb
ridiz
atio
n &
Liga
tion
Liga
tion
Hyb
ridiz
atio
n ♦
base
-pai
ring
betw
een
two
com
plem
enta
ry si
ngle
-stra
nd
mol
ecul
es to
form
a d
oubl
e st
rand
ed D
NA
mol
ecul
e
Liga
tion
♦Jo
inin
g D
NA
mol
ecul
es to
geth
er
Solu
tion
gene
ratio
n st
ep!
(C) 2
002,
SN
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/23
CGTA
CCTT
AGG
CT
CGTA
CCTT
AGG
CTAG
CTTA
GG
ATG
GCA
TGG
AATC
CGAT
GCA
TGG
C
CGTA
CCTT
AGG
CTAG
CTTA
GG
ATG
GCA
TGG
AATC
CGAT
GCA
TGG
C
AGCT
TAG
GAT
GG
CATG
GAA
TCCG
ATG
CATG
GC
+
Liga
tion
Hyb
ridi
zatio
n
Deh
ybri
diza
tion
DN
A H
ybrid
izat
ion
& D
NA
Hyb
ridiz
atio
n &
Liga
tion
AGCT
TAG
GAT
GG
CATG
GAA
TCCG
ATG
CATG
GC
+
Liga
tion
CGTA
CCTT
AGG
CT
(C) 2
002,
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PCR
PCR
Poly
mer
ase
Cha
in R
eact
ion
Am
plifi
es (p
rodu
ces i
dent
ical
cop
ies o
f) se
lect
ed
dsD
NA
mol
ecul
es.
Mak
e 2n
copi
es (n
: num
ber o
f ite
ratio
n)
Solu
tion
filte
ring
or a
mpl
ifica
tion
step
!
(C) 2
002,
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PCR
PCR
(Pol
ymer
ase
Cha
in R
eact
ion)
(Pol
ymer
ase
Cha
in R
eact
ion)
(C) 2
002,
SN
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Gel
Ele
ctro
phor
esis
Gel
Ele
ctro
phor
esis
Mol
ecul
ar si
ze fr
actio
n te
chni
que
Det
ect t
he sp
ecifi
c D
NA
Bead
Sep
arat
ion
Bead
Sep
arat
ion
Solu
tion
dete
ctio
n or
filte
ring
step
!
(C) 2
002,
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Gel
Ele
ctro
phor
esis
Gel
Ele
ctro
phor
esis G
el im
age
(C) 2
002,
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Mag
netic
Bea
ds
Mag
net
Com
plem
enta
ry
Bead
Sep
arat
ion
Bead
Sep
arat
ion
(C) 2
002,
SN
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Res
trict
ion
Enzy
mes
Res
trict
ion
Enzy
mes
Cut
the
spec
ific
DN
A si
te.
Solu
tion
dete
ctio
n or
filte
ring
step
!
A A
G C
T T
T T
C G
A A
A T T
C G
A
A C
G T
T A
OH
3’
3’O
H
5’P
P 5’
EcoR
I
DN
A C
ompu
ting
of H
PPD
NA
Com
putin
g of
HPP
(C) 2
002,
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The
Firs
t Spe
cial
DN
A C
ompu
ter
The
Firs
t Spe
cial
DN
A C
ompu
ter
Spec
ial p
robl
em: g
iven
N p
oint
s, fin
d a
path
vi
sitin
g ea
ch a
nd e
very
poi
nt o
nly
once
, and
st
artin
g an
d en
ding
at a
giv
en lo
catio
ns.
(Ham
ilton
ian
path
pro
blem
)So
lved
with
a D
NA
com
pute
r by
Leon
ard
Adl
eman
in 1
994
for N
=6B
asic
app
roac
h: c
ode
each
poi
nt a
s an
8 un
it D
NA
st
ring,
cod
e ea
ch p
ossi
ble
path
, allo
w D
NA
bo
ndin
g, su
ppre
ss D
NA
with
inco
rrec
t sta
rt/en
d po
ints
.
(C) 2
002,
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Ham
ilton
ian
Path
Pro
blem
Ham
ilton
ian
Path
Pro
blem
The
Ham
iltoi
anpa
th p
robl
em: a
s th
e nu
mbe
r of c
ities
gro
ws,
even
su
perc
ompu
ters
hav
e di
fficu
lty
findi
ng th
e pa
th.
10
3
25
6
4
(C) 2
002,
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Adle
man
Adle
man
’’ ssM
olec
ular
Com
pute
r: M
olec
ular
Com
pute
r: A
Brut
e Fo
rce
Met
hod
A Br
ute
Forc
e M
etho
dEach c
ity
(vertex)
is
repre
sente
d b
y a
diffe
rent se
quence o
f nucle
otides
(6 h
ere
, but Adle
man
use
d 2
0).
A D
NA lin
ker
(edge)
join
ing tw
o c
ity
(vertex)
strands.
(C) 2
002,
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Enco
ding
(Bas
ic C
once
pt)
Enco
ding
(Bas
ic C
once
pt)
1
32
AGCT
TAG
GP 1
AP 1
B
ATG
G C
ATG
P 2A
P 2B
CGAT
CG
AAP 3
AP 3
B
P 1B
P 3A
PP 2
A
13 2
56
4
ATCC
TAC
CAT
CC G
CTA
0
1B
(C) 2
002,
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Proc
edur
ePr
oced
ure
thro
ugh
the
grap
h
inan
d en
d w
ith v
out
PCR w
ith v
inan
d v o
ut
Gel
ele
ctro
phor
esis
Gel
ele
ctro
phor
esis
&
Antib
ody
bead
sep
arat
ion
With
vi
Gen
erat
e ra
ndom
pat
hs
Hyb
ridiz
atio
n &
Lig
atio
n
Keep
onl
y th
ose
path
s th
at
If t
he g
raph
has
n v
ertic
es,
then
kee
p on
ly t
hose
pat
hs
that
ent
er e
xact
ly n
ver
tices
Keep
onl
y th
ose
path
s th
at
of t
he g
raph
at
leas
t on
ce.
begi
n w
ith v
ente
r al
l of
the
vert
ices
If a
ny p
aths
rem
ain,
say
“Ye
s”;
othe
rwis
e, s
ay “
No.
”Se
quec
ing
(C) 2
002,
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AGCT
TAG
G
ATCC
TACC
ATG
GCA
TG
56 b
p
Ver
tex
1V
erte
x 2
Edge
1→
216
bp
Step
4 :
Gel
Ele
ctro
phor
esis
AGCT
TAG
GAT
GG
CATG
GAA
TCCG
A…TC
GAA
Step
1 :
Hyb
ridi
zatio
nAT
CCTA
CCAG
CTTA
GG
ATG
GCA
TG
TCC
Bead
for v
erte
x 1
Affi
nity
Sep
arat
ion
ATG
GCA
TGAG
CTTA
GG
ATCC
TACC
Step
2 :
Liga
tion
Step
5 :
Mag
netic
Bea
d
AGCT
TAG
GAT
GG
CATG
GAA
TCCG
ATG
CATG
GC
TCG
AATC
C
Ver
tex
1
ACG
TACC
G
Ver
tex
4
Step
3 :
PCR
(C) 2
002,
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in
Rea
ctio
n)
AC
GC
GA
GC
ATA
AA
TGTG
CC
GT
AC
GC
GA
GC
ATA
AA
TGTG
CC
GT
AC
GC
GT
AG
CC
GT
...
AC
GC
GA
GC
AT
AA
AT
GC
GA
TG
CC
GT
......
Gel
Ele
ctro
phor
esis
Affi
nity
Col
umn
HPP
...
......
...
ATG
ATG
AC
GA
CG
TGC
TGC C
GA
CG
ATA
ATA
AG
CA
GC
AC
GT
CG
T ......
...
......
...
......
10
3 25
6
4So
lutio
n
PCR
(Pol
ymer
ase
AT
GT
GC
TA
AC
GA
AC
G
AC
GC
GA
GC
ATA
AA
TGTG
CC
GT
AC
GC
GA
GC
ATA
AA
TGTG
CC
GT
TA
AA
CG
CG
AC
GT
TA
AA
CG
GC
AA
CG
...
...
...
...
CG
AC
GT
AG
CC
GT
...
...
AC
GC
GA
GC
AT
AA
AT
GC
GA
TG
CA
CG
C
... AC
GC
GT
...
......
...
AC
GG
CA
TA
AA
TG
TG
CA
CG
CG
T
AC
GC
GA
GC
ATA
AA
TGTG
CC
GT
AC
GC
GA
GC
ATA
AA
TGTG
CC
GT
......
......
...
AC
GC
GA
GC
ATA
AA
TGTG
CC
GT
AC
GC
GA
GC
ATA
AA
TGTG
CC
GT
......
...
Dec
odin
g
Liga
tion
Enco
ding
AC
GC
GA
GC
AT
AA
AT
GT
GC
AC
GC
GT
GT
AC
GC
GA
GC
AT
AA
AT
GT
GC
AC
GC
GT
AC
GC
GA
GC
AT
AA
AT
GC
GA
TG
CA
CG
CG
T
2
01
34
5
6
Nod
e 0
: AC
GN
ode
3 : T
AA
Nod
e 1
: CG
AN
ode
4 : A
TGN
ode
2 : G
CA
Nod
e 5
: TG
CN
ode
6 : C
GT
(C) 2
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DN
A Fi
nds
a So
lutio
n!D
NA
Find
s a
Solu
tion!
A H
amilt
onia
n pa
th w
ith a
ll ve
rtic
es in
clud
ed is
is
olat
ed a
nd re
cove
red
Anot
her P
ract
ical
Exa
mpl
e:An
othe
r Pra
ctic
al E
xam
ple:
Mol
ecul
ar T
heor
em P
rovi
ngM
olec
ular
The
orem
Pro
ving
(C) 2
002,
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Mol
ecul
ar T
heor
em
Mol
ecul
ar T
heor
em P
rove
rPr
over
Reso
lutio
n re
futa
tion
met
hod
RQ
P∨
¬∨¬
QT
S∨
¬∨¬
ST
PR¬
RQ∨
¬Q
T∨¬
Q
R
nil
R is
tru
e!
Prob
lem
und
er
cons
ider
atio
n:
Turn
into
, a
dd R
as
?tru
e ,
, ,
,=
→∧
→∧
RP
TS
QT
SR
QP
BA→
BA∨
¬
R¬
RP
TS
QT
SR
QP
¬∨
¬∨
¬∨
¬∨
¬ ,
, ,
,
(C) 2
002,
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Mol
ecul
ar T
heor
em
Mol
ecul
ar T
heor
em P
rove
rPr
over
(Abs
trac
t Im
plem
enta
tion)
(Abs
trac
t Im
plem
enta
tion)
¬S¬T
Q
¬Q¬P
R
P¬R
TS ¬S
¬TQ ¬Q
¬PRP
¬R
TS
¬S¬T
Q ¬Q¬P
RP
¬RT
S
(C) 2
002,
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Expe
rimen
tal P
roce
dure
Expe
rimen
tal P
roce
dure
Step
1. D
NA
Seq
uenc
e D
esig
nSt
ep 2
. DN
A S
ynth
esis
Step
3. C
hem
ical
Rea
ctio
n in
a T
est T
ube
♦H
ybrid
izat
ion
♦Li
gatio
n
Step
4. D
etec
tion
of S
olut
ions
♦PC
R♦
Gel
Ele
ctro
phre
sis
(C) 2
002,
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Sequ
ence
Des
ign
¬Q
∨¬P
∨R
:5’
3’
Q ∨
¬T ∨
¬S:
3’5’
S
: 5’
3’
T
: 3’
ATT G
AC
GC
A A
AT T
GA
5’
P
: 5’
3’ 3’TG
Sequ
ence
Des
ign
CG
T A
CG
TAC
GC
T G
AA C
TG
CC
T T
GC
GTT G
AC
TG
C G
TT C
AT T
GT A
TG
GTC
AAC
GC
A A
GG
CAG
R
: 5’
¬R :
3’5’
TTC
AG
C G
TA C
GT A
CG
AAG
CAG
TAG
CG
A
TC
A A
TT T
GC
GTC
AAT T
GG
TC
G C
TA C
TG
CTT
CC
A
CAT A
CA A
TG
AAC
GC
A
TG
C G
TT C
AT T
GT A
(C) 2
002,
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Rea
ctio
n in
a T
est T
ube
Rea
ctio
n in
a T
est T
ube
R ∨
¬ P∨
¬ QS
Q ∨
¬T ∨
¬ST
P ¬R
(C) 2
002,
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Rea
ctio
n in
a T
est T
ube
Rea
ctio
n in
a T
est T
ube
Q ∨
¬T ∨
¬ST
P
R ∨
¬ P∨
¬ QS
¬R
(C) 2
002,
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Rea
ctio
n in
a T
est T
ube
Rea
ctio
n in
a T
est T
ube
R ∨
¬ P∨
¬ QS
¬R
Q ∨
¬T ∨
¬ST
P
(C) 2
002,
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Rea
ctio
n in
a T
est T
ube
Rea
ctio
n in
a T
est T
ube
R ∨
¬ P∨
¬ QS
Q ∨
¬T ∨
¬ST
P ¬R
(C) 2
002,
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Rea
ctio
n in
a T
est T
ube
Rea
ctio
n in
a T
est T
ube
R ∨
¬ P∨
¬ QS
Q ∨
¬T ∨
¬ST
P ¬R
(C) 2
002,
SN
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Rea
ctio
n in
a T
est T
ube
Rea
ctio
n in
a T
est T
ube
Q ∨
¬T ∨
¬ST
P
R ∨
¬ P∨
¬ Q¬R
S
(C) 2
002,
SN
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Rea
ctio
n in
a T
est T
ube
Rea
ctio
n in
a T
est T
ube
R ∨
¬ P∨
¬ QS
Q ∨
¬T ∨
¬ST
P ¬R
(C) 2
002,
SN
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Hyb
ridiz
atio
n an
d H
ybrid
izat
ion
and
Liga
tion
Liga
tion
(C) 2
002,
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Hyb
ridiz
atio
n an
d H
ybrid
izat
ion
and
Liga
tion
Liga
tion
G C
GT C
AG
TTG
CG
T T
CC
GTC
AAG
TC
G C
AT G
CA T
GC
¬Q AC
A A
TG
AAC
GC
A
AC
C A
GC
GAT G
AC
GAA
SG
TA T
GT T
AC
TT
TTC
AG
C G
TA C
GT A
CG
TC
A A
TT T
GC
GTC
AAT T
GG
TC
G C
TA C
TG
CTT
Q ∨
¬T ∨
¬S
AG
T T
AA A
CG
CAG
TTA
TG
TC
AAC
GC
A A
GG
CAG
P
¬R
R ∨
¬P∨C
AT
(C) 2
002,
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Hyb
ridiz
atio
n an
d H
ybrid
izat
ion
and
Liga
tion
Liga
tion
GTA T
GT T
AC
TTG
CG
T C
AG
TTG
CG
T T
CC
GTC
AAG
TC
G C
AT G
CA T
GC
R ∨
¬P∨
¬Q
CAT A
CA A
TG
AAC
GC
A
¬R AC
C A
GC
GAT G
AC
GAA
S
TTC
AG
C G
TA C
GT A
CG
TC
A A
TT T
GC
GTC
AAT T
GG
TC
G C
TA C
TG
CTT
Q ∨
¬T ∨
¬SAG
T T
AA A
CG
CAG
TTA
TG
TC
AAC
GC
A A
GG
CAG
P
(C) 2
002,
SN
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Hyb
ridiz
atio
n an
d H
ybrid
izat
ion
and
Liga
tion
Liga
tion
GTA T
GT T
AC
TTG
CG
T C
AG
TTG
CG
T T
CC
GTC
A
R ∨
¬P∨
¬Q
CAT A
CA A
TG
AAC
GC
A
¬RTTC
AG
GTC
AAC
GC
A A
GG
CAG
P
AG
TC
G C
AT G
CA T
GC
AC
C A
GC
GAT G
AC
GAA
S
C G
TA C
GT A
CG
TC
A A
TT T
GC
GTC
AAT T
GG
TC
G C
TA C
TG
CTT
∨¬T
∨¬S
AG
T T
AA A
CG
CAG
TTA
T
Q
(C) 2
002,
SN
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Mol
ecul
ar T
heor
em
Mol
ecul
ar T
heor
em P
rove
r20
bp
DM
A m
arke
r (
Prov
er
Exp
erim
enta
l S
teps
Results
II.
II.
Den
atu
rati
onD
enat
ura
tion
( 9
5(
95
°° C 1
0 m
in)
C 1
0 m
in)
gel E
lect
roph
ores
is(2
0%)
gel E
lect
roph
ores
is(2
0%)
( P
AG
E )
( P
AG
E )
V. D
etec
tion
of
solu
tion
V. D
etec
tion
of
solu
tion
: 7
5bp
:
75
bp d
sds
DN
AD
NA
III.
An
nea
ling
III.
An
nea
ling
C 1
min
C
1 m
in
15
15 °°
C :
1C
: 1
°° C d
own
/min
C
dow
n/m
in
I. M
IXI.
MIX
100
100
pmol
pmol
/eac
h
/eac
h
Tota
l 20
Tota
l 20
ul
ul
200
200
11
Tala
ra)
Mix
ture
Rea
ctio
n
223
45
6 63
45
bpbp
IV.
IV.
Pol
yacr
ylam
ide
Pol
yacr
ylam
ide
9595°°
20
20 b
pbp
The
Diff
icul
ties
of D
NA
Com
pute
rTh
e D
iffic
ultie
s of
DN
A C
ompu
ter
(C) 2
002,
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The
Rea
lity
of D
NA
Base
d Th
e R
ealit
y of
DN
A Ba
sed
Com
puta
tion
Com
puta
tion
Sym
met
ry m
akes
con
trol d
iffic
ult.
Impo
rtanc
e of
Non
-Wat
son-
Cric
k Pa
iring
.Im
porta
nce
of h
ybrid
izat
ion
prot
ocol
s.Im
porta
nce
of c
once
ntra
tion
and
envi
ronm
ent.
Fide
lity
of li
gatio
nD
NA
mol
ecul
es b
reat
h.is
hig
h, b
ut N
OT
perf
ect.
(C) 2
002,
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The
Rea
lity
of D
NA
Base
d Th
e R
ealit
y of
DN
A Ba
sed
Com
puta
tion
Com
puta
tion
Aff
inity
bin
ding
is a
filtr
atio
n pr
oces
s.C
ompl
ex li
gatio
npr
oduc
es c
ompl
ex p
rodu
cts.
Res
trict
ion
enzy
mes
pro
duce
s par
tial d
iges
tion
prod
ucts
.B
ase
stac
king
is o
ften
dete
rmin
ing
inte
ract
ion.
DN
A is
a p
hysi
cal c
hem
ical
syst
em.
(C) 2
002,
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Enco
ding
Pro
blem
sEn
codi
ng P
robl
ems
Enco
ding
Pro
blem
s♦
enco
ding
pro
blem
is m
appi
ng th
e pr
oble
m in
stan
ce
onto
a se
t of D
NA
mol
ecul
es a
nd m
olec
ular
bio
logy
pr
otoc
ols s
o th
at th
e re
sulti
ng p
rodu
cts c
onta
in a
n an
swer
to in
stan
ce o
f the
pro
blem
♦pr
even
t err
ors
♦en
able
ext
ract
ion
(C) 2
002,
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Ope
ratio
nal P
robl
ems
Ope
ratio
nal P
robl
ems
It ta
kes T
OO
long
tim
es♦
hybr
idiz
atio
n/lig
atio
n op
erat
ion
over
4 h
ours
♦In
Adl
eman
’s e
xper
imen
ts :
7 da
ys!
(C) 2
002,
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Ope
ratio
nal P
robl
ems
Ope
ratio
nal P
robl
ems
Not
Per
fect
Ope
ratio
n♦
Hyb
ridiz
atio
n M
ism
atch
es♦
Extra
ctio
n Er
rors
♦V
olum
e an
d M
ass t
o so
lve
a pr
oble
m
Fals
e N
egat
ives
Fals
e Po
sitiv
es
(C) 2
002,
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Hyb
ridiz
atio
n M
ism
atch
esH
ybrid
izat
ion
Mis
mat
ches
Rel
iabi
lity
: Fal
se P
ositi
ves a
nd N
egat
ives
Effic
ienc
y
AGG
CTTA
GCT
TCCA
GAT
CGA
Mis
mat
ched
Hyb
ridiz
atio
n
AGG
CTA C C G
TTTC
C
Hai
rpin
Hyb
ridiz
atio
n
AGG
CTTA
GCT
CGAA
TCG
AGC
Shift
ed H
ybrid
izat
ion
(C) 2
002,
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Det
ectio
n Pr
oble
ms
Det
ectio
n Pr
oble
ms
NO
T ex
act d
etec
tion
Gel
ele
ctro
phor
esis
is w
idel
y us
ed d
etec
tion
tech
niqu
e.♦
We
can
not s
epar
ate
the
exac
t sol
utio
n!
(C) 2
002,
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Sour
ces
of E
rrors
Sour
ces
of E
rrors
a) C
omm
on o
pera
tion
in h
andl
ing
DN
A is
filte
ring:
DN
A fi
lter
5% e
rror
rat
eH
eter
ogen
ous
mix
Sing
le D
NA
solu
tion
Lead
s to
high
out
put e
rror
rate
b) C
hain
Rea
ctio
n fo
r DN
A a
mpl
ifica
tion.
erro
rA
TTG
A..
ATG
GA
..
Rar
e ty
pe o
f err
or, b
ut d
oes p
rese
nt a
pro
blem
(C) 2
002,
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c) B
indi
ng e
rror
. Exp
ect b
indi
ng b
etw
een
com
plem
ents
Form
atio
n of
doub
le h
elix
CT
GA
T
GA
CC
Aer
ror
caus
es b
ulge
s, m
isse
d bo
nds -
-tr
ansl
ates
into
out
put e
rror
s
Erro
r res
ilien
t com
puta
tion
tech
niqu
es re
quire
d:♦
clas
sic
erro
r cor
rect
ion
with
redu
ndan
t rep
rese
ntat
ion
♦ca
refu
l dat
a en
codi
ng -
trade
off
den
sity
for r
esili
ency
♦va
ryin
g en
viro
nmen
t con
ditio
ns m
ay im
prov
e pe
rfor
man
ce
Que
stio
n: a
re e
rror
s alw
ays b
ad ?
In
this
cas
e, a
n oc
casi
onal
m
utat
ion
may
lead
to im
prov
ed le
arni
ng
Sour
ces
of E
rrors
Sour
ces
of E
rrors
DN
A C
ompu
ting
Appl
icat
ions
DN
A C
ompu
ting
Appl
icat
ions
(C) 2
002,
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Appl
icat
ions
of
Appl
icat
ions
of B
iom
olec
ular
Biom
olec
ular
Com
putin
gC
ompu
ting
Mas
sive
ly p
aral
lel p
robl
em so
lvin
gC
ombi
nato
rial o
ptim
izat
ion
Mol
ecul
ar n
ano-
mem
ory
with
fast
ass
ocia
tive
sear
chA
I pro
blem
solv
ing
Med
ical
dia
gnos
is, d
rug
disc
over
yC
rypt
ogra
phy
Bio
com
pute
rFu
rther
impa
ct in
bio
logy
and
med
icin
e:
♦W
et b
iolo
gica
l dat
a ba
ses
♦Pr
oces
sing
of D
NA
labe
led
with
dig
ital d
ata
♦Se
quen
ce c
ompa
rison
♦
Fing
erpr
intin
g
(C) 2
002,
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DN
A Ad
der
DN
A Ad
der
[UC
Ber
kely
, USA
]
The
Add
ition
Rea
ctio
n: P
rimer
Ext
ensi
on
Poly
mer
ase
Tem
plat
e D
NA
Prim
er D
NA
(= 2
nddi
git)
3’5’
5’Pr
imer
Ext
ensi
on
(C) 2
002,
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e La
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Mas
sive
ly P
aral
lel T
heor
em
Mas
sive
ly P
aral
lel T
heor
em
Prov
ing
Prov
ing
[War
saw
Uni
v. o
f Tec
hnol
ogy,
Pol
and]
A B
DC
A
D
AB
CB
B
D
C
A
IF Premise THEN Conclusion
Prem
ise
Conc
lusi
on
(C) 2
002,
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Brea
king
DES
Brea
king
DES
[Prin
ceto
n, U
SA]
B1(
0)
S 0
B1(
1)
S 1
B2(
0)
B2(
1)B
N(1
)
BN(0
)
S N…
..
DE
S ci
rcui
t ini
tial g
raph
S 0l
S 0r
S 1l
S 1r
S Nl
S Nr
S 0l
S 0r
S 1l
S 1r
S Nl
S Nr
B1l (0
)B1r (0
)B
2l (1)B
2r (1)
B1l (0
)B
1r (0)
B2l (1
)B
2r (1)
S 2l
BN
r (1)
A p
ath
in th
e gr
aph
Futu
re A
pplic
atio
nsFu
ture
App
licat
ions
(C) 2
002,
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a) S
elf-
repl
icat
ion:
Tw
o fo
r one
Bas
ed o
n D
NA
self-
repl
icat
ion
b) S
elf-
repa
ir:B
ased
on
rege
nera
tion
c) D
NA
com
pute
r m
utat
ion/
evol
utio
n
or
bioh
azar
d
Lea
rnin
g.
May
be
mal
igna
nt
d) N
ew m
eani
ng o
f aco
mpu
ter v
irus ?
Inte
rest
ing
Poss
ibilit
ies
Inte
rest
ing
Poss
ibilit
ies
(C) 2
002,
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Evol
vabl
e Ev
olva
ble
Biom
olec
ular
Bi
omol
ecul
ar
Har
dwar
eH
ardw
are
Sequ
ence
pro
gram
mab
le a
nd e
volv
able
mol
ecul
ar sy
stem
s hav
e be
en
cons
truct
ed a
s cel
l-fre
e ch
emic
al sy
stem
s usi
ng b
iom
olec
ules
such
as
DN
A a
nd p
rote
ins.
(C) 2
002,
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ioin
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e La
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Mol
ecul
ar S
tora
ge fo
r Mas
sive
ly
Mol
ecul
ar S
tora
ge fo
r Mas
sive
ly
Para
llel I
nfor
mat
ion
Ret
rieva
lPa
ralle
l Inf
orm
atio
n R
etrie
val
Trill
ions
of D
NA
Hon
olul
u, H
I64
8-79
21Pa
ul
La Jo
lla, C
A.
352-
4730
Dav
id
Was
hing
ton
DC
419-
1332
Jam
es
Add
ress
Tel.
Nam
e
Palo
Alto
CA
418-
9362
Julia
…
Phon
e bo
ok
(C) 2
002,
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e La
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Mol
ecul
ar C
ompu
ter o
n a
Chi
pM
olec
ular
Com
pute
r on
a C
hip
Det
ectio
nD
etec
tionM
icro
reac
tor
Mic
rore
acto
rPC
RPC
RG
el E
lect
roph
ores
isG
el E
lect
roph
ores
is
Bea
dB
ead
DN
A co
mpu
ting
algo
rithm
MEM
S (M
icro
fluid
ics)
+
Real
DN
A co
mpu
ter
(C) 2
002,
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ioin
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e La
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BioM
EMS
BioM
EMS
: The
Nex
t Tra
nsis
tors
: The
Nex
t Tra
nsis
tors
(C) 2
002,
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ioin
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e La
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Inte
grat
es sa
mpl
e ha
ndlin
g,
sepa
ratio
n an
d de
tect
ion
and
data
ana
lysi
s for
: DN
A,
RN
Aan
d pr
otei
nso
lutio
ns
usin
g L
abC
hip
tech
nolo
gy.
Lab
Lab --
onon-- aa
-- Chi
p Te
chno
logy
Chi
p Te
chno
logy
(C) 2
002,
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Con
clus
ion
Con
clus
ion
DN
A c
ompu
ting
uses
DN
A m
olec
ules
for
com
putin
g or
as s
tora
ge m
ater
ials
.D
NA
com
putin
g te
chno
logy
has
man
y in
tere
stin
g pr
oper
ties,
incl
udin
g♦
Mas
sive
ly p
aral
lel,
solu
tion-
base
d, b
ioch
emic
al♦
Min
iatu
rized
, nan
o-sc
ale,
bio
com
patib
le♦
Hig
h en
ergy
eff
icie
ncy
♦
Hig
h m
emor
y st
orag
e de
nsity
DN
A c
ompu
ting
is in
a v
ery
early
stag
e of
de
velo
pmen
t.
(C) 2
002,
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ioin
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e La
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/70
Res
earc
h Pr
ojec
ts/G
roup
sR
esea
rch
Proj
ects
/Gro
ups
MIT
, Cal
tech
, Prin
ceto
n U
nive
rsity
, Bel
l Lab
s EM
CC
(Eur
opea
n M
olec
ular
Com
putin
g C
onso
rtium
) is
com
pose
d of
nat
iona
l gro
ups f
rom
11
Euro
pean
cou
ntrie
s B
ioM
IPIn
stitu
te(B
ioM
olec
ular
Info
rmat
ion
Proc
essi
ng)
at th
e G
erm
an N
atio
nal R
esea
rch
Cen
ter f
or In
form
atio
n Te
chno
logy
(GM
D)
Mol
ecul
ar C
ompu
ter P
roje
ct (M
CP)
in Ja
pan
Leid
enC
ente
r for
Nat
ural
Com
puta
tion
(LC
NC
) M
olec
ular
Evo
lutio
nary
Com
putin
g (M
EC) P
roje
ct in
K
orea
, Seo
ul N
atio
nal U
niv.
(C) 2
002,
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ioin
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e La
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nu.a
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/71
Web
Res
ourc
esW
eb R
esou
rces
Euro
pean
Mol
ecul
ar C
ompu
ting
Con
sorti
um(E
MC
C):
http
://w
ww
.csc
.liv.
ac.u
k/~e
mcc
/B
ioM
olec
ular
Info
rmat
ion
Proc
essi
ng(B
ioM
ip):
http
://w
ww
.gm
d.de
/BIO
MIP
Le
iden
Cen
ter f
or N
atur
al C
ompu
tatio
n(L
CN
C):
http
://w
ww
.wi.l
eide
nuni
v.nl
/~lc
nc/
Bio
mol
ecul
arC
ompu
tatio
n (B
MC
): ht
tp://
bmc.
cs.d
uke.
edu/
DN
A C
ompu
ting
and
Info
rmat
ics a
t Sur
face
s:
http
://w
ww
.cor
ninf
o.ch
em.w
isc.
edu/
writ
ings
/DN
Aco
mpu
ting
.htm
l SN
U M
olec
ular
Evo
lutio
nary
Com
putin
g (M
EC) P
roje
ct:
http
://bi
.snu.
ac.k
r/Res
earc
h/
(C) 2
002,
SN
U B
ioin
telli
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e La
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nu.a
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/72
Book
sBo
oks
Cris
tian
S, C
alud
ean
d G
heor
ghe
Paun
, Com
putin
g w
ith C
ells
and
A
tom
s: A
n in
trod
uctio
n to
qua
ntum
, DN
A a
nd m
embr
ane
com
putin
g,
Tayl
or &
Fra
ncis
, 200
1.Pâ
un, G
., Ed
., C
ompu
ting
With
Bio
-Mol
ecul
es: T
heor
y an
d E
xper
imen
ts, S
prin
ger,
1999
.G
heor
ghe
Paun
, Grz
egor
z R
ozen
berg
and
Arto
Sal
omaa
, DN
A
Com
putin
g, N
ew C
ompu
ting
Para
digm
s, Sp
ringe
r, 19
98.
C. S
. Cal
ude,
J. C
asti
and
M. J
. Din
neen
, Unc
onve
ntio
nal M
odel
s of
Com
puta
tion,
Spr
inge
r, 19
98.
Tono
Gra
mss
, Ste
fan
Bor
nhol
dt, M
icha
el G
ross
, Mel
anie
Mitc
hell
and
thom
as P
elliz
zari,
Non
-Sta
ndar
d C
ompu
tatio
n: M
olec
ular
C
ompu
tatio
n-C
ellu
lar A
utom
ata-
Evo
lutio
nary
Alg
orith
ms-
Qua
ntum
C
ompu
ters
, Wile
y-V
ch, 1
997.
