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Near-Perfect Adaptation in Bacterial Chemotaxis. Yang Yang and Sima Setayeshgar Department of Physics Indiana University, Bloomington, IN. Chemotaxis Signal Transduction Network in E. coli. Stimulus. Signal Transduction Pathway. [CheY-P]. Motor Response. Flagellar Bundling. - PowerPoint PPT Presentation
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March 8, 2007 Yang Yang, March APS Meeting, Denver, CO 1
Near-Perfect Adaptation in Bacterial Chemotaxis
Yang Yang and Sima Setayeshgar
Department of Physics
Indiana University, Bloomington, IN
Chemotaxis Signal Transduction Network in E. coli
March 8, 2007 Yang Yang, March APS Meeting, Denver, CO
2
Histidine kinase Methylesterase
Couples CheA to MCPs Response regulator
Methyltransferase Dephosphorylates CheY-P
CheB
CheW
CheZ
CheR
CheY
Signal Transduction
Pathway
Motor Response
[CheY-P]
Stimulus
Flagellar Bundling
Motion
Run Tumble
Robust Perfect Adaptation
March 8, 2007 Yang Yang, March APS Meeting, Denver, CO
Fast response Slow adaptation
From Sourjik et al., PNAS (2002).
FRET signal [CheY-P]
From Alon et al., Nature (1999).
CheR fold expressionAd
apta
tio
n
Pre
ciso
n
Steady state [CheY-P] / running bias independent of value constant external stimulus (adaptation)
Precision of adaptation insensitive to changes in network parameters (robustness)
This Work: Outline
March 8, 2007 Yang Yang, March APS Meeting, Denver, CO 4
New computational scheme for determining conditions and numerical ranges for parameters allowing robust (near-)perfect adaptation in the E. coli chemotaxis network
Comparison of results with previous works
Extension to other modified chemotaxis networks, with additional protein components
Conclusions and future work
E. coli Chemotaxis Signaling Network
March 8, 2007 Yang Yang, March APS Meeting, Denver, CO 5
Ligand binding
Methylation
Phosphorylation
)()( )(7~5
7~5)( CheRLTCheRTL pn
kmkm
kkpn
ppnmkmk
ppn
pnckck
pn
CheBTLCheBTL
CheRTLCheRTL
)(14~1
)(
)(14~1
)(
)()(
)()(
PCheBCheB
PCheYCheZCheZCheY
CheBCheRTCheBCheRTL
CheYCheRTCheYCheRTL
ADPCheRTLATPCheRTL
kmbp
kmyp
pnkb
np
nky
np
npkk
n
)()()(
)()()(
)()()()( 9~7T3 T4T2
T2p T4pT3p
LT3 LT4
LT4p
LT2
LT3pLT2p
phosphorylation
methylation
Lig
an
d b
ind
ing
Approach …
March 8, 2007 Yang Yang, March APS Meeting, Denver, CO 6
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 CheY-P
values of reaction rate constants,
are independent of the external stimulus, s, thereby explicitly incorporating perfect adaptation.
s
k
F
u
skuFdt
ud
0);;(
: state variables
: reaction kinetics
: reaction rates
: external stimulus
The steady state concentration of proteins in the network satisfy:
The steady state concentration of = [CheY-P] must be independent of stimulus, s:
where parameter allows for “near-perfect” adaptation.
Reaction rates are constant and must also be independent of stimulus, s:
Augmented System
March 8, 2007 Yang Yang, March APS Meeting, Denver, CO 7
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
0ds
kd
0);;( skuFdt
ud
||ds
duN
Nu
Discretize s in
range {slow, shigh}
Physical Interpretation of Parameter, : Near-Perfect Adaptation
March 8, 2007 Yang Yang, March APS Meeting, Denver, CO 8
Measurement of c = [CheY-P] by flagellar motor constrained by diffusive noise Relative accuracy*,
Signaling pathway required to adapt “nearly” perfectly, to within this lower bound
(*) Berg & Purcell, Biophys. J. (1977).
%101
~
cDac
c
: diffusion constant (~ 3 µM)
: linear dimension of motor C-ring (~ 45 nm)
: CheY-P concentration (at steady state ~ 3 µM)
: measurement time (run duration ~ 1 second)c
a
D
},,{ kuy
Use Newton-Raphson (root finding algorithm with back-tracking), to solve for the steady state of augmented system,
Use Dsode (stiff ODE solver), to verify time- dependent behavior for different ranges of external stimulus by solving:
Implementation
0
||
0);(
ds
kdds
dysyF
N
);;( skuFdt
ud
March 8, 2007 Yang Yang, March APS Meeting, Denver, CO 9
T4 demethylation rate (km2)
T4
aut
oph
osp
hory
latio
n ra
te
(k10
)
LT2 methylation rate (k3c)
LT
4 a
uto
ph
osp
ho
ryla
tion
ra
te
(k10
)
Parameter Surfaces
March 8, 2007 Yang Yang, March APS Meeting, Denver, CO 10
● 3%<<5% ● 1%<<3% ● 0%<<1%
Surface: 2D projections:
)(
|)()(|
beforeY
beforeYafterY
p
pp
Validation
March 8, 2007 Yang Yang, March APS Meeting, Denver, CO 11
Time (s)
Co
nce
ntr
atio
n (
µM
)Verify steady state NR solutions dynamically using DSODE for different stimulus ramps:
{k3c= 5 s-1, k10 = 101 s-1, km2 = 6.3e+4 M-1s-1}
1%
k1c : 0.17 s-1 1 s-1
k8 : 15 s-1 12.7 s-1
Violating and Restoring Perfect Adaptation
March 8, 2007 Yang Yang, March APS Meeting, Denver, CO 12
Step stimulus from 0 to 1e-6M at t=250s
(1,15)
(1,12.7)
T2 Methylation rate (k1c)
T2
auto
phos
phor
ylat
ion
rate
(k
8)
Conditions for Perfect Adaptation
Methylation Rate Autophosphorylation Rate
March 8, 2007 Yang Yang, March APS Meeting, Denver, CO 14
T2 autophosphorylation rate (k8)
T2 M
eth
yla
tion
ra
te (
k 1c)
T3 autophosphorylation rate (k9)
T3 M
eth
yla
tion
ra
te (
k 2c)
LT2 autophosphorylation rate (k12)
LT
2 M
eth
yla
tion
ra
te (
k 3c)
LT3 autophosphorylation rate (k13)
LT
3 M
eth
yla
tion
ra
te (
k 4c)
Demethylation Rate Autophosphorylation Rate2
March 8, 2007 Yang Yang, March APS Meeting, Denver, CO 15
T3 autophosphorylation rate (k9)
T3 d
em
eth
yla
tion
ra
te (
k m1)
T4 autophosphorylation rate (k10)
T4 d
em
eth
yla
tion
ra
te (
k m2)
LT3 autophosphorylation rate (k12)
LT
3 d
em
eth
yla
tion
ra
te (
k m3)
LT4 autophosphorylation rate (k13)
LT
4 d
em
eth
yla
tion
ra
te (
k m4)
Demethylation Rate/Methylation Rate Autophosphorylation Rate
March 8, 2007 Yang Yang, March APS Meeting, Denver, CO 16
T3 autophosphorylation rate
T3
dem
ethy
latio
n ra
te/ T
2 m
ethy
latio
n ra
te
T4 autophosphorylation rate
T4
dem
ethy
latio
n ra
te/ T
3 m
ethy
latio
n ra
te
LT3 autophosphorylation rate
T3
dem
ethy
latio
n ra
te/ T
2 m
ethy
latio
n ra
te
LT4 autophosphorylation rate
LT4
dem
ethy
latio
n ra
te/ L
T3
met
hyla
tion
rate
CheB, CheY Phosphorylation Rate Autophosphorylation Rate
March 8, 2007 Yang Yang, March APS Meeting, Denver, CO 17
Che
B p
hosp
hory
latio
n ra
te (
k b)
/ lit
erat
ure
val
ue
Che
Y p
hosp
hory
latio
n ra
te (
k y)
/ lit
erat
ure
val
ue
(L)Tn autophosphorylation rate / literature value (L)Tn autophosphorylation rate / literature value
● T2● T3● T4● LT3● LT4
● T2● T3● T4● LT3● LT4
Che
B p
hosp
hory
latio
n ra
te
LT2 autophosphorylation rate
Che
Y p
hosp
hory
latio
n ra
te
LT2 autophosphorylation rate
Diversity of Chemotaxis Systems
March 8, 2007 Yang Yang, March APS Meeting, Denver, CO 18
Eg., Rhodobacter sphaeroides, Caulobacter crescentus and several rhizobacteria possess multiple CheYs while lacking of CheZ homologue.
In different bacteria, additional protein components as well as multiple copies of certain chemotaxis proteins are present.
Response regulator
Phosphate “sink”
CheY1CheY2
Two CheY System
March 8, 2007 Yang Yang, March APS Meeting, Denver, CO 19
Exact adaptation in modified chemotaxis network with CheY1, CheY2 and no CheZ:
Ch
eY1
p (µ
M)
Ch
eY1
p (µ
M)
Time(s) Time(s)
Requiring: Faster phosphorylation/autodephosphorylation rates of CheY2 than CheY1
Faster phosphorylation rate of CheB
Conclusions
March 8, 2007 Yang Yang, March APS Meeting, Denver, CO 20
I. Successful implementation of a novel method for elucidating regions in parameter space allowing precise adaptation
II. Numerical results for (near-) perfect adaptation manifolds in parameter space for the E. coli chemotaxis network, allowing determination of
i. conditions required for perfect adaptation, consistent with and extending previous works [1-3]
ii. numerical ranges for unknown or partially known kinetic parameters
I. Extension to modified chemotaxis networks, for example with no CheZ homologue and multiple CheYs
[1] Barkai & Leibler, Nature (1997). [2] Yi et al., PNAS (2000). [3] Tu & Mello, Biophys. J. (2003).
Future Work
March 8, 2007 Yang Yang, March APS Meeting, Denver, CO 21
Extension to other signaling networks
vertebrate phototransduction mammalian circadian clock
allowing determination of
a) parameter dependences underlying robustness
b) plausible numerical values for unknown network parameters