Transcript Slide 1

Receptor clustering
and signal processing
in E.coli Chemotaxis
Ref.1----TRENDS in Microbiology Vol.12 No.12 December 2004
Ref.2----PNAS Vol. 102 No. 48 November 2005
Binding
Attractant
Decrease
Increase
Higher
Methylation
level
Decrease
Lower
Methylation
level
CheA Activity
Binding
Repellent
Increase
short re-orientations (or tumbles)
counterclockwise (CCW)
smooth swimming (or runs)
clockwise (CW)
Three interesting points:
1. The high sensitivity
2. Wide dynamic range
3. Integration of multiple stimuli of this
pathway
Cooperative Protein Interactions in Receptor Clusters
Computer Modeling
Quantitative Experimental Analysis
Model of the higher-order structure of a receptor cluster. (a,b) Receptor homodimers
(Tsr, black; Tar, gray; Trg, yellow) are thought to form trimers that, in the absence of
CheA and CheW, appear as loose caps at cell poles. CheA and CheW assemble
into signalling complexes with trimers to form tight receptor clusters at the pole
through a combination of receptor–receptor, receptor–CheW, receptor–CheA,
CheA–CheW, and possibly CheW–CheW interactions. (c,d) In fluorescence images,
receptor localization is visualized with fluorescently-tagged CheR.
The high sensitivity and wide dynamic range
As little as 10nM aspartate
Less than 10 molecules of
aspartate in a volume of an E.
coli cell
Estimated to change the
receptor
occupancy by 0.2%
Resulted in a 23%
change in the BIAS of
motor rotation, indicating
signal AMPLIFICATION
(or gain) by a factor of
~100
Moreover, at least for some attractants,
cells retain high sensitivity over
variations of five orders of
magnitude of ambient attractant
concentrations.
Kinds of Models
Two-state model
Assumption 1:The receptor exists in two conformational states, active or
inactive, which either promote or inhibit the activity of
associated CheA
Assumption 2:The receptor–kinase complex is stable on the timescale of the
chemotactic response and kinase associated with active
receptor is always active and vice versa.
Assumption 3: A cluster consists of independent receptor–kinase complexes
and changes in their activity directly reflect changes in receptor
occupancy. It is thus unable to explain signal amplification.
Allosteric models of multi-subunit receptor–kinase
complexes
Assumption 1(Key):The inactive state of a receptor homodimer has a higher
affinity to attractant than the active state.
Assumption 2:
The inactive state can be stabilized by either attractant
binding or the conformational states of neighbouring
receptors.
Some properties:
1.The sensitivity of the response therefore grows dramatically with increasing
numbers of subunits.
2. A complex of interacting receptors thus has a tendency to exhibit a switch-like
behaviour. If activity of such a complex (or its subunits) in absence of ligand is
moderate, binding of attractants to only a few receptors stabilizes the entire
complex in the inactive state. By contrast, if the initial bias toward the active
state is high, the complex does not make the transition to the inactive state until
most subunits are occupied, producing a steep response with a large Hill
coefficient.
3. In a mixed allosteric receptor complex, addition of aspartate increases the
sensitivity to serine, and vice versa .
Derived
from
the
model
High
sensitivity in
wide dynamic
range
The bias of the
complex to an active
state is moderate
Role of
Methylation
System
To
sence
Change of the ligand
concentration
Tune
and
keep
Feedback through
the methylation
system in wild-type
cells
Cause
Things to be done?
Experimentally, the physical nature of these interactions remaims
obscure. Nor is it clear how receptor clusters localize to the cell poles
and whether localization of signalling proteins in bacteria is a general
feature or a special feature of chemotaxis.
On the modelling side, allosteric models of receptor interactions in the
receptor–kinase complex, when combined with kinetic models of the
cytoplasmic part of the pathway, are able to account for most
observations in chemotaxis, but they still have to be ‘tuned’ to match
experimental data more closely. Especially, how does the methylation
level affect the parameters in the model.
MWC model by using an Hamiltonian approach
The complex is made of N identical subunits, each of which can bind to a
ligand molecule.
The ligand occupancy of the ith subunit is given by σi, σi=0, 1 for vacant and
occupied receptor, respectively (i=1, 2, . . . , N).
In the all-or-none MWC model, the activity s of the complex is either active
(s=1) or inactive (s=0).
For the MWCmodel, the energy of the complex depends on s and σi in the
following way:


H   E    i s    i
i
i


E is the energy difference between the active and inactive state in the
absence of ligand;
each occupied receptor suppresses the activity by increasing the energy of
the active state by ε>0;
μ is the energy for ligand binding for the inactive state and depends on the
ligand concentration and a dissociation constant, Ki, for the inactive state.
All energies are in units of the thermal energy kBT.
The correspondence between the energy parameters used here and that of
the original MWC model can be summarized in the following:
e
E
L
e

C
e


L

Ki
[L] is the ligand concentration.
The dissociation constant for the active state, Ka, is simply given by: Ka=Ki/C.
L is the equilibrium constant.
Given the Hamiltonian, the partition function Z is given by:
Z
 N
E
 (   ) N
exp(

H
)

(
1

e
)

e
(
1

e
)

all .states
From the partition function, all of the steady-state (equilibrium) properties of
the model can be easily calculated. In particular, the average activity <s>
can be determined:
N
L
(
1

C
[
L
]
/
K
)

Z
1
i
 s  Z

E (1  [ L] / Ki ) N  L(1  C[ L] / Ki ) N
N1
N2
N1
N2


H m   E   1   i1   2   i2  s  1   i1   2   i2
i1 1
i2 1
i1 1
i2 1


N j ,1
N j,2

[ L1 ]  
[ L2 ] 
 1  C2

L j 1  C1
K1  
K2 

( 0)
F j ([L]1 , [ L]2 )  A j 
N j ,1
N j,2
N j ,1
N j,2
 [ L1 ]   [ L2 ] 

[L ]  
[L ] 
1 
 1 
  L j 1  C1 1  1  C2 2 
K1  
K2 
K1  
K2 


exp(-E)=L，exp(-ε1)=C1，exp(-μ1)=[L1]/K1，exp(-ε2)=C2，exp(-μ2)=[L2]/K2
N j ,1 : N j ,2  f j ,1 : f j ,2
E. coli CheRB-- mutant with different
induced Tar and Tsr expression levels
j(strain)
fj,1
fj,2
Nj,1
Nj,2
Aj(0)
------------------------------------------------------------------------------1
0.6
2
4.95
16.5
0.0806
2
1
2
4.00
8.00
0.0933
3
2
2
4.39
4.39
0.118
4
6
2
18.7
6.24
0.0875
5
1
0
14.0
0
0.0323
6
2
0
29.8
0
0.0645
7
6
0
73.5
0
0.0872
8
0
0.6
0
9.85
0.0133
9
0
1.4
0
15.2
0.0365
10
0
10
0
32.3
0.0983
------------------------------------------------------------------------------The receptor-specific parameters are found to be l1=1.23, C1=0.449, K1
49.2(μM) for Tar; and l2=1.54, C2=0.314, K2=34.5(μM) for Tsr.