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March 8, 2007 March APS Meeting, Denver, CO 1
Near-Perfect Adaptation in Bacterial Chemotaxis
Yang Yang and Sima Setayeshgar
Department of Physics
Indiana University, Bloomington, IN
March 8, 2007 March APS Meeting, Denver, CO 2
Chemotaxis in E. coli
http://www.rowland.harvard.edu/labs/bacteria/index_movies.html
Increasing attractants / decreasing repellent
Run TumbleCourtesy of Howard Berg Lab
March 8, 2007 March APS Meeting, Denver, CO 3
Chemotaxis Signal Transduction Network in E. coli
;
CheB
CheW
CheZ
CheR
CheY
March 8, 2007 March APS Meeting, Denver, CO 4
Robust Perfect Adaptation
March 8, 2007 March APS Meeting, Denver, CO 5
This Work: Outline New computational scheme for determining
conditionsnumerical ranges
for parameters allowing robust (near-)perfect adaptation in the context of the E. coli chemotaxis network
Comparison of results with previous works
Extension to other chemotaxis networks, with additional protein components
Conclusions and future work
March 8, 2007 March APS Meeting, Denver, CO 6
Ligand binding
Methylation
Phosphorylation
)()( )(7/7~5/5
)( CheRLTCheRTL pnkmkkmk
pn
ppnmkmk
ppn
pnckck
pn
CheBTLCheBTL
CheRTLCheRTL
)(14~1
)(
)(14~1
)(
)()(
)()(
PCheBCheB
PCheYCheZCheZCheY
CheBCheRTCheBCheRTL
CheYCheRTCheYCheRTL
ADPCheRTLATPCheRTL
kmbp
kmyp
pnkb
np
nky
np
npkk
n
)()()(
)()()(
)()()()( 9~7
T3 T4T2
T4pT2p T3p
LT3 LT4
LT4p
LT2
LT3pLT2p
phosphorylation
methylation
Liga
nd b
indi
ng
Biochemical Signaling Network
March 8, 2007 March APS Meeting, Denver, CO 7
START with a fine-tuned model of chemotaxis network that:
reproduces key features of experiments
is NOT robust
AUGMENT the model explicitly with the requirements that: steady state value of CheYp
values of reaction rate constants,
are independent of the external stimulus, s, thereby achieving robustness of perfect adaptation.
s
k
F
u
skuFdt
ud
0);;(
: state variables
: reaction kinetics
: reaction constants
: external stimulus
Numerical Scheme
March 8, 2007 March APS Meeting, Denver, CO 8
Decretizing s
into H points
0
||
0);;(
ds
kdds
du
skuFdt
ud
N
02
|2
|
0);;(
)1(
11
11
s
kks
uu
skuFdt
ud
sjss
jm
jm
j
jN
jN
jjj
jlowj
Augmented systemThe steady state concentration of proteins in the network must satisfy:
The steady state concentration of CheYp must satisfy:
At the same time, the reaction rate constants must be independent of stimulus:
: allows for near-perfect adaptation
= CheYp
0ds
kd
0);;( skuFdt
ud
N
N
u
ds
du
||
March 8, 2007 March APS Meeting, Denver, CO 9
Near-perfect Adaptation
ImplementationNewton-Raphson, to solve for the steady state of augmented system:
0
||
0);;(
ds
kdds
du
skuFdt
ud
N
Dsode (stiff ODE solver), to verify Time dependent behavior of proteins for different ranges of external stimulus by solving:
0);;( skuFdt
ud
March 8, 2007 10March APS Meeting, Denver, CO
Pairwise result: 3D surface result:
Relative change of CheYp:• less than 5% and greater than 3%• less than 3% and greater than 1%• less than 1%• pairwise trajectory
E .coli
Auto
phosp
hory
lati
on r
ate
of
T4
(k
10
)
LT2 methylation rate (k3c)
Auto
phosp
hory
lati
on r
ate
of
T4
(k
10
)
T4 demethylation rate (km2)
parameter spaces of E. coli
March 8, 2007 11March APS Meeting, Denver, CO
DSODE solutions for NR parameters set(3)
March 8, 2007 March APS Meeting, Denver, CO 12
1%
k1c : 0.17 s-1 1 s-1
k8 : 15 s-1 12.7 s-1
Violating and restoring perfect adaptation
At 250s, giving step stimulus from 0 to 1e-6M
(1,15)
(1,12.7)
Methylation rate of T2 (k1c)
Auto
phosp
hory
lati
on r
ate
of
T2 (
k8)
March 8, 2007 13March APS Meeting, Denver, CO
Condition 2
Autophosphorylation rate of LT2 (k12)
Meth
yla
tion r
ate
of
LT2
(k
3c)
Autophosphorylation rate of T2 (k8)
Meth
yla
tion r
ate
of
T2
(k1
c)
Autophosphorylation rate of LT3 (k13)
Meth
yla
tion r
ate
of
LT3
(k
4c)
Autophosphorylation rate of T3 (k9)
Meth
yla
tion r
ate
of
T3
(k2
c)
Methylation rate autophosphorylation rate
Condition 2-continue
Autophosphorylation rate of T3 (k9)
Dem
eth
yla
tion r
ate
of
T3
(k
m1)
Autophosphorylation rate of T4 (k10)
Dem
eth
yla
tion r
ate
of
T4
(k
m2)
Autophosphorylation rate of LT3 (k12)
Dem
eth
yla
tion r
ate
of
LT3
(k
m3
)
Autophosphorylation rate of LT4 (k13)
dem
eth
yla
tion r
ate
of
LT4
(k
m4
)
demethylation rate (autophosphorylation rate)2
Condition 4demethylation rate/phosphorylation rate
autophosphorylation rate
T3 autophosphorylation rate
T3
dem
eth
yla
tion
rate
/ T2
meth
yla
tion
ra
te
T4 autophosphorylation rate
T4
dem
eth
yla
tion
rate
/ T3
meth
yla
tion
ra
te
LT3 autophosphorylation rate
T3
dem
eth
yla
tion
rate
/ T2
meth
yla
tion
ra
te
LT4 autophosphorylation rate
LT4
dem
eth
yla
tion
rate
/ LT
3 m
eth
yla
tion
ra
te
Condition 5
*The parameter value are normalized to the literature value( Peter A. S., John S.P. and Hans G.O. , A model of excitation and adaptation in bacterial chemotaxis, biochemistry 1997) while the inset is not since the literature value is zero
CheB
phosp
hory
lati
on
rate
/ lit
era
ture
valu
e
CheY p
hosp
hory
lati
on
rate
/ lit
era
ture
valu
e
(L)Tn autophosphorylation rate / literature value(L)Tn autophosphorylation rate / literature value
● T2● T3● T4● LT3● LT4
● T2● T3● T4● LT3● LT4
Ch
eB
ph
osp
hory
lati
on
rate
LT2 autophosphorylation rate
Ch
eY p
hosp
hory
lati
on
rate
LT2 autophosphorylation rate
CheB, CheY phosphorylation rate autophosphorylation rate
March 8, 2007 March APS Meeting, Denver, CO 18
Two CheY system
•Rhodobacter sphaeroides, Caulobacter crescentus have multiple CheYs while lack of CheZ protein.•Similar chemotaxis behaviors.
Two CheY system
Our work:Reproduce the key feature of chemotaxis behavior in two CheY system by replacing CheZ with CheY2.
Ch
eY1
p (µ
M)
Ch
eY1
p (µ
M)
Time(s) Time(s)
parameter spaces comparison of two and
single CheY case
parameter spaces comparison of two and
single CheY case
parameter spaces comparison of two and
single CheY case
parameter spaces comparison of two and
single CheY case
March 8, 2007 March APS Meeting, Denver, CO 24
Conclusions
Complete construction of manifolds in parameter space, allowing insight into parameter dependence giving rise to robustness
Work in progress
March 8, 2007 March APS Meeting, Denver, CO 25
Future work• Applying the method to other cellular signal
transduction networks exhibiting robust homeostasis, such as phototransduction
Signal flow in visual transduction, Leon Lagnado and Denis Baylor,Neuron,1992
March 8, 2007 March APS Meeting, Denver, CO 26
Conclusions Successful implementation of a novel method for elucidating regions in parameter space allowing precise adaptation
Preliminary results for two- and three-dimensional projections of (near-) perfect adaptation manifolds in parameter space for the E. coli chemotaxis network, allowing determination of
conditions required for perfect adaptation, consistent with previous works numerical ranges for unknown or partially known kinetic parameters
Extension to modification of the E. coli chemotaxis network, consistent with absence of CheZ homolog and presence of multiple CheY copies in rhizobacteria
March 8, 2007 March APS Meeting, Denver, CO 27
Future Work