Receptor clustering and signal processing in E.coli ChemotaxisRef.1----TRENDS in Microbiology Vol.12 No.12 December 2004

Ref.2----PNAS Vol. 102 No. 48 November 2005

Binding Attractant

CheA Activity

Binding Repellent

Lower Methylation level

Higher Methylation level

Increase

IncreaseDecrease

Decrease

smooth swimming (or runs)

counterclockwise (CCW) clockwise (CW)

short re-orientations (or tumbles)

1. The high sensitivity

2. Wide dynamic range

3. Integration of multiple stimuli of this pathway

Three interesting points:

Computer Modeling Quantitative Experimental Analysis

Cooperative Protein Interactions in Receptor Clusters

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 receptoroccupancy 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 ofmagnitude of ambient attractant concentrations.

Kinds of Models

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.

Two-state model

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.

Allosteric models of multi-subunit receptor–kinase complexes

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 .

The bias of the complex to an active state is moderate

High sensitivity in wide dynamic range

Feedback through the methylation system in wild-type cells

Tune and keep

Change of the ligand concentration

Cause

To sence

Derived from the model

Role of Methylation System

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.

Things to be done?

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:

MWC model by using an Hamiltonian approach

ii

ii sEH

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:

Le E Ce iK

Le

[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:

NEN

statesall

eeeHZ )1()1()exp( )(

.

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:

Ni

Ni

Ni

KLCLKL

KLCL

E

ZZs

)/][1()/][1(

)/][1(1

2,1,2,1,

2,1,

2

22

1

11

2

2

1

1

2

22

1

11

)0(21

][1

][1

][1

][1

][1

][1

)][,]([jjjj

jj

NN

j

NN

NN

j

jj

K

LC

K

LCL

K

L

K

L

K

LC

K

LCL

ALLF

1

1

2

2

21

1

1

2

2

211 1

211 1

21

N

i

N

iii

N

i

N

iiim sEH

exp(-E)=L ， exp(-ε1)=C1 ， exp(-μ1)=[L1]/K1 ， exp(-ε2)=C2 ， exp(-μ2)=[L2]/K2

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-------------------------------------------------------------------------------

2,1,2,1, :: jjjj ffNN E. coli CheRB-- mutant with different induced Tar and Tsr expression levels

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.