Modeling the chemosensing system of E. coli

Ned Wingreen – PrincetonJuan Keymer – Princeton

Robert Endres – Princeton/NECYigal Meir – Ben Gurion University

Outline• Introduction to chemotaxis in E. coli

– Runs and tumbles – Signaling properties– The chemotaxis network

• FRET – New probe of receptor activity– Two regimes of activity– Receptors function collectively

• Modeling• How does adaptation work?

Signaling properties of the chemotaxis network

• “Precise and robust adaptation”: range of 3-4 orders of magnitude of attractant

• “Signal integration”: multiple attractants

• “Sensitivity”: amplification

Segall, Block, and Berg (1986)

CCW vs CW bias for tethered cells in response to step in attractant

The chemotaxis networkht

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……but signal integration and sensitivity but signal integration and sensitivity are still not well understood.are still not well understood.

Chemoreceptors

Tar - aspartate, glutamate (~900 copies)Tsr - serine (~1600)Trg - ribose, galactose (~150)Tap - dipeptides (~150)(Aer - oxygen via FAD (150?))

Methyl binding sitesCheB, CheR

Sensor

Linker region

Cytoplasmicdomain

CheA / CheWbinding region

Stock (2000)

Dimer

•Attractant binding inhibits phosphorylation of CheA

•Adaptation: More attractant → increased methylation by CheR → increased rate of phosphorylation of CheA

Less attractant → increased demethylation by CheB → decreased rate of phosphorylation of CheA

Transmembrane Transmembrane heliceshelices

380 A

Chemoreceptor clustering

Receptors are clustered globally into a large array, and locally into trimers of dimers.

Ges

twic

ki

Ges

twic

ki e

t al.

et a

l. (2

000)

(200

0)

Kim Kim et al. et al. (1999); Studdert (1999); Studdert and Parkinson (2004)and Parkinson (2004)

In vivo FRET studies of receptor activity

Sourjik and Berg (2002)Sourjik and Berg (2002)

Real-time measurement of rate of phosphorylation of CheY.

FRET also allows subcellular imaging, Vaknin And Berg (2004).

Sourjik and Berg (2002)Regime I:• Activity moderate to low at zero ambient MeAsp (0.06,1)• KD small and almost constant

Regime II:• Activity high (saturated?) at zero ambient MeAsp (1.3-1.9)• KD1 large and increasing with methylation• Plateau in activity• KD2 approximately constant

FRET data: two regimes of activity

Regime I

Regime II

Two regimes of receptor activity consistent with 2-state receptor model.

• Originally proposed by Asakura and Honda (1984).• Modified by Barkai and Leibler (1998) to explain precise and

robust adaptation: – Receptor complex has 2 states: “on”, i.e. active as kinase,

and “off”, i.e. inactive as kinase.– Demethylation only occurs in “on” state, i.e. when receptor is

active, so that

– Therefore, at steady state,

– Which implies precise and robust adaptation of each receptor complex to a fixed activity.

2-state receptor model

Activity[CheB]-CheR][nMethylatio badt

d

[CheB]/[CheR] Activity baBarkai and Leibler (1997)

Regime I:• Activity low to very low at zero ligand concentration • KD = KD

off

Regime II:• Activity high (saturated) at zero ligand concentration• KD increasing as εon ↓

offoffon

on

off

onActivity

eKCee

eP

D

Two regimes of a 2-state receptor

However, single receptor does not account for low apparent KD in Regime I.

On OffOff

Regime I Regime II

On

Off

On

Off

Off Off

Ligand Ligand

Free Energy

But first, a “1-state” receptor:

Ligand

KD

DKC

P

1

1bound ligand no

On

offon

off

on ,11

1Activity)(

N

K

C

D

NeP Regime I (Δε > 0):

• Low activity ~ e-NΔε at zero ligand concentration• KD = KD

off / N

• Hill coefficient = 1

Regime II (Δε < 0):• KD = KD

off e-Δε

• Hill coefficient = N

Receptor-receptor couplingDuke and Bray (1999)

Duke and Bray (1999) proposed that receptor-receptor coupling could enhance sensitivity to ligands.

Toy model: if N receptors are all “on” or all “off” together,

Receptor-receptor coupling gives enhanced sensitivity (low KD) in Regime I, and enhanced cooperativity (high Hill coefficient ) in Regime II.

Regime I• Low, constant KD

• Activity low at zero ligand concentration• Hill coefficient ≈ 1

Regime II:• KD1 increasing with methylation• Activity high at zero ligand concentration• Hill coefficient ≈ 1 ?• Plateau in activity ?

Review of FRET data

= KDoff

/N, value of N ?

Hill coefficient increases with receptor homogeneity.

Must consider mixture of different receptor types.

Sourjik and Berg (2004)

More Tars

Less Tars

Regime I: • KD set by coupling energy EJ

Regime II:• Plateaus: Tars “off”, Tsrs “on” • Hill coefficient ≈ 1, no cooperativity because Tar receptors separated by Tsr receptors

Model: 1d mixed lattice of receptorsN

orm

aliz

ed A

ctiv

ity

Log([MeAsp])

TsrTarEJ

Receptors are in Regime II:

• Hill coefficient increases with homogeneity because clusters of identical receptors grow.

• KD (or KD1) increases as lattice becomes more mixed because of coupling EJ to “on” receptors.

Receptor homogeneity and cooperativity

Nor

mal

ized

Act

ivity

Log([MeAsp])

More Tars

Less Tars

Adaptation

Adaptation uses methylation to return all receptors to Δε ≈ 0, and thereby enhances sensitivity.

TsrTar

Δε ≈ 0 Off

Δε > 0 Δε > 0 Δε > 0Δε ≈ 0 Δε ≈ 0 Δε ≈ 0

Precise adaptation

Scaling of wild-type response data

Sourjik and Berg: Δ[MeAsp] → ΔFRET{Tar(QEQE)}

Sou

rjik

and

Ber

g (2

002)

ΔFRET for Tar(QEQE) strain

“Free energy” scaling: Δ[MeAsp] → Δ(Fon – Foff)

Doesn’t collapse zero-ambient data.

Includes zero-ambient data!

Predictions

For homogeneous lattice –

• Transition from Regime I to Regime II with methylation

• Adaptation range set by KDon

Sourjik (unpublished)MeAsp

Act

ivity

Open questions

• Lattice structure?

• Mechanism of receptor-receptor coupling?

• Do other receptors work this way?

Sto

ck (2

000)

Conclusions• Signaling properties of the chemotaxis network:

– Precise and robust adaptation– Signal integration– Sensitivity

• FRET studies reveal two regimes of activity– Regime I: low activity and constant KD

– Regime II: high activity and increasing KD• Model of coupled 2-state receptors account for signaling

properties, and for two regimes– Regime I (Δε > 0): coupling → enhanced sensitivity– Regime II (Δε < 0): coupling → enhanced

cooperativity (but only for homogeneous clusters)• Adaptation “homogenizes” receptors (Δε ≈ 0) for

enhanced sensitivity