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Transcript of Turing Meets Synthetic Biology - 2009.igem.org2009.igem.org/files/poster/IPN-UNAM-Mexico.pdf ·...
Turing M
eets
Synth
etic B
iolo
gy
We p
rese
nt a
syn
theti
c ne
twor
k th
at e
mul
ates
an a
ctiv
ator
-inh
ibit
or s
yste
m. O
ur g
oal is
to
show
that
spa
tiot
em
pora
l st
ruct
ures
can
be g
ene
rate
d b
y th
e b
ehav
ior
of a
gene
tic
regu
lato
ry n
etw
ork.
We im
plem
ent
the m
odel by
mean
s of
seve
ral bio
bri
cks.
We
cons
truc
t a
self
act
ivat
ing
mod
ule a
nd c
orre
spon
din
gly
an inh
ibit
ory
one. S
elf
-act
ivat
ion
dyn
amic
s is
giv
en
by
the L
as o
pero
n,
while t
he inh
ibit
ory
part
is
prov
ided b
y th
e L
ux o
pero
n. Q
uoru
m s
ens
ing
and d
iffu
sion
of
AH
L p
rovi
de t
he r
eac
tion
-dif
fusi
on m
e-
chan
ism
resp
onsi
ble
for
the f
orm
atio
n of
Tur
ing
patt
ern
s. T
he im
port
ance
of
our
wor
k re
lies
on t
he f
act
that
we s
how
that
the
acti
on o
f th
e m
orph
ogene
s as
ori
gina
lly
prop
osed b
y T
urin
g is
equ
ival
ent
to
the e
ffect
of
dif
fusi
on o
f ch
em
ical
s in
tera
ctin
g w
ith
the s
ynth
eti
c ne
twor
k, w
hic
h a
ccou
nts
for
the r
eac
tive
par
t, a
pos
sibilit
y im
plic
it in
Tur
ing‛
s or
igin
al w
ork
in t
he c
onte
xt
of m
or-
phog
ene
sis
of b
iolo
gica
l pa
ttern
s.
Se
lf-e
me
rgin
g p
att
ern
s in
an
ac
tiv
ato
r-in
hib
ito
r n
etw
ork
.
ABSTRACT
Bas
ed o
n th
e d
esi
gn o
f th
e b
iobri
cks
netw
ork
we t
ried t
o m
odel th
e b
ehav
ior
it w
ould
hav
e w
ithin
a s
ingl
e
cell. T
o do
this
we c
onst
ruct
ed t
he k
ineti
c la
ws
desc
ribin
g th
e r
ela
tion
ship
s betw
een
the c
ompo
nent
s of
ou
r ne
twor
k an
d I
PTG
and
aT
c. W
e m
odele
d t
he i
ntera
ctio
ns o
f th
e A
HL‛s
wit
h t
heir
resp
ect
ive t
arge
ts
as a
llos
teri
c re
gula
tors
aff
ect
ing
the p
roduc
tion
rat
e o
f th
e c
atal
yzin
g enz
ymes,
thus
aff
ect
ing
the s
yn-
thesi
s of
the A
HL‛s
. This
cat
alys
is w
as a
ssum
ed t
o be a
fir
st o
rder
kine
tics
depe
ndin
g on
ly o
n th
e c
once
n-tr
atio
n of
the c
atal
yst.
The d
iffu
sion
rat
e o
f th
e A
HL‛s
was
reduc
ed t
o a
firs
t or
der
kine
tics
con
sideri
ng
the m
em
bra
ne a
rea
of t
he b
acte
ria
and a
ssum
ing
the c
ompl
ete
abse
nce o
f th
e A
HL o
utsi
de t
he c
ell, t
here
-fo
re d
epe
ndin
g on
ly o
n th
e p
roduc
tion
wit
hin
the c
ell.
Luis
J. M
art
íne
z Lo
me
li*,
Je
sús
Pé
rez
Juá
rez*
, Da
nie
l I. A
gu
ila
r S
alv
ad
or*
, Gil
be
rto
Gó
me
z C
orr
ea
*, J
osé
Ma
rtín
ez
Lom
eli
*, C
rist
ian
J. D
elg
ad
o G
*, F
ran
cisc
o J
. Ra
zo H
ern
án
de
z*,
Ile
an
a d
e la
Fu
en
te C
olm
en
are
s, A
lin
Acu
ña
Alo
nzo
, Ro
má
n A
. Aco
sta
Día
z, E
nia
k H
ern
an
de
z, P
ab
lo P
ad
illa
Lo
ng
ori
a, A
lex
an
de
r d
e L
un
a F
ors
, Fa
bio
la R
am
ire
z C
oro
na
, Art
uro
Be
cerr
a, F
ran
cisc
o H
ern
án
de
z Q
uir
oz,
Elí
as
Sa
mra
.
Tur
ing
form
ally
desc
ribed h
is p
ropo
sal w
ith a
set
of p
arti
al d
iffe
rent
ial equ
atio
ns w
here
is
poss
ible
to
re-
prese
nt t
he c
hem
ical
int
era
ctio
ns o
f th
e m
orph
ogens
and
the w
ay t
hey
mov
e o
ver
the s
pace
. T
his
kin
d o
f dyn
amic
s ar
e c
omm
only
cal
led r
eac
tion
-dif
fusi
on m
ech
anis
ms,
and
the e
quat
ions
that
desc
ribe t
hem
are
na
med R
eac
tion
-Dif
fusi
on e
quat
ions
:
React
ion-
Diffu
sion
equ
ation
s
In 1
97
2 A
. Gie
rer
and H
. Mein
har
dt
publish
ed t
heir
wor
k ca
lled “
A t
heor
y of
bio
logi
cal p
atte
rn f
orm
atio
n”
prese
ntin
g a
netw
ork
bas
ed in
the int
era
ctio
n of
at
leas
t tw
o m
orph
ogens
act
ing
as a
n ac
tiva
tor
and a
n in
-hib
itor
. The m
ain
qual
itat
ive d
ynam
ics
of t
he m
orph
ogens
is “
shor
t ra
nge a
ctiv
atio
n, lo
nger
rang
e in
hib
itio
n an
d a
con
cept
ual dis
tinc
tion
betw
een
eff
ect
ive c
once
ntra
tion
s of
act
ivat
or a
nd inh
ibit
or, on
one
han
d, an
d
the d
ens
ity
of t
heir
sou
rces
on t
he o
ther”
.
The A
ctivato
r-Inh
ibitor
Act
ivato
r-Inh
ibitor
dyna
mics
on a
single c
ell
Gie
rer
an
d M
ein
ha
rdt
Kin
eti
cs
No
nd
ime
ns
ion
al
Gie
rer
an
d M
ein
ha
rdt
Kin
eti
cs
Spa
tial M
odel
Est
imate
d D
iffu
sion
Con
stant
s
Expe
riment
al W
ork
To
do
this
we c
onsi
dere
d t
he m
olecu
lar
weig
ht
of t
he A
HL m
olecu
les
and w
e e
stim
ated t
he d
iam
ete
r of
th
e m
olecu
les
taki
ng int
o ac
coun
t th
e lin
ear
str
uctu
re o
f th
em
. F
rom
the a
rtic
les
of A
. E
inst
ein
: “O
n th
e
Mot
ion
Requ
ired b
y th
e M
olecu
lar
Kin
eti
c T
heor
y of
Heat
of
Sm
all
Part
icle
s S
uspe
nded i
n a
Sta
tion
ary
Liq
uid”
and “
A n
ew
dete
rmin
atio
n of
mol
ecu
lar
dim
ens
ions
” w
e u
sed t
he m
eth
od t
o est
imat
e t
he d
iffu
sion
co
eff
icie
nts
from
the d
iam
ete
r of
the m
olecu
le u
sing
the m
odif
ied f
rict
ion
coeff
icie
nt o
f th
e w
ater
in
prese
nce o
f gl
ucos
e t
o im
prov
e t
he a
ccur
acy
as d
esc
ribed.
We m
ade a
sim
ulat
ion
wit
h v
alue
s pr
evi
ousl
y us
ed b
y J
.D. M
urra
y an
d t
he p
revi
ousl
y est
imat
ed d
iffu
sion
coe
ffic
ient
s of
PA
I a
nd A
I m
olecu
les
wit
h t
he
reac
tion
-dif
fusi
on e
quat
ions
of
the G
iere
r an
d M
ein
har
dt
mod
el.
The s
imul
atio
n w
as m
ade i
n a
circ
ular
ar
ea
wit
h z
ero
flu
x b
ound
ary
cond
itio
ns a
nd a
ll t
he p
aram
ete
rs v
alue
s fo
und in
the lit
era
ture
.
Aft
erw
ard w
e d
esc
ribed a
s or
din
ary
dif
fere
ntia
l equ
atio
ns t
he t
ime c
han
ge o
f th
e c
once
ntra
tion
s of
PA
I
and A
I bas
ed o
n th
e k
ineti
c la
w e
quat
ions
, bein
g “X
” PA
I an
d “
Y”
AI.
Wit
h t
his
sys
tem
of
dif
fere
ntia
l equ
atio
ns d
esc
ribin
g th
e k
ineti
c bas
is o
f th
e r
eac
tion
and
dif
fusi
on w
e p
roce
eded t
o m
ake a
qua
lita
tive
an
alys
is o
f it
s behav
ior.
Dur
ing
this
mon
ths
we a
com
plis
hed t
he s
ynth
esi
s of
11
new
bio
bri
cks
(pro
tein
gene
rato
rs a
nd i
nvert
ers
) w
hic
h w
ere
add t
o th
e R
egi
stry
, w
e h
ave t
he 9
0%
of
adva
nce o
f ou
r sy
stem
com
plete
d a
s fo
llow
s.
We a
lso
hav
e p
reelim
inay
dat
a co
nfir
min
g th
e p
ropp
er
func
tion
ing
of t
he a
ctiv
ator
mod
ule, as
show
in
the
pict
ures.
No IPTG
160 mM IPTG
Con
clus
ions
and
fur
ther
wor
kT
he p
relim
inar
y re
sult
s sh
ow t
hat
the a
ctiv
ator
sys
tem
wor
ks. T
he inh
ibit
or w
ill be c
oupl
ed b
y th
e e
nd o
f th
e y
ear
. In
order
to p
erf
orm
the e
xpe
rim
ent
s to
show
if
our
bio
bri
cks
syst
em
is
able
to
prod
uce a
n sp
a-ti
otem
pora
l pa
ttern
, w
e w
ill us
e a
chem
ical
gra
die
nt o
f IP
TG
and
aT
c. T
he m
odeling
resu
lts
hav
e g
iven
us
an ins
ight
of h
ow t
he s
yste
m w
ill re
spon
d t
o pa
rtic
ular
chem
ical
ini
tial
dis
trib
utio
ns.
Besi
des
we a
lso
need t
o co
mpl
ete
the m
odellin
g pa
rt o
f th
e p
roje
ct w
ith d
iffe
rent
pers
pect
ives.
T
he u
se
of s
toch
asti
c ap
proa
ches
shou
ld a
llow
us
to int
roduc
e n
oise
in
the s
yste
m a
nd loo
k how
the e
merg
enc
e o
f bac
teri
a pa
ttern
cou
ld b
e a
ffect
ed.
We a
re n
ot s
o fa
r to
con
clud
e if
an a
ctiv
ator
-inh
ibit
or m
ech
anis
m im
plem
ent
ed w
ith b
iobri
cks
coul
d g
ene
-ra
te a
spa
tiot
em
pora
l tu
ring
lik
e p
atte
rn.
Main r
efe
renc
es
-Tur
ing
A. M
., "T
he C
hem
ical
Bas
is o
f M
orph
ogene
sis"
, Ph
ilos
ophic
al T
rans
acti
ons
of T
he R
oyal
Soc
iety
of
Lon
don
, se
ries
B, 2
37
:37
–72
, 19
52
-Gie
rer
A. an
d M
ein
har
dt
H.,
"A t
heor
y of
bio
logy
cal pa
ttern
for
mat
ion"
, K
ybern
eti
k 12
:30
-39
, 19
72
-Mur
ray
J.D
., "M
athem
atic
al B
iolo
gy I
I",
Spr
inge
r-V
erl
ag B
erl
in H
eid
elb
erg
, 3
rd e
dit
ion,
19
93
Init
ial
inst
abilit
y dam
ping
by
the s
inui
dal
ini
tial
con
dit
ion
of d
ynam
ical
sys
tem
sim
ulat
ion.
The s
yste
m e
volu
tion
lead
to
an
nonh
omog
ene
ous
stat
e b
ut a
n sp
atia
l gr
adie
nt.
€
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