Modeling the chemosensing system of E. coli Ned Wingreen – Princeton Juan Keymer – Princeton Robert Endres – Princeton/NEC Yigal 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) J. E. Segall, S. M. Block, and H. C. Berg, Proc Natl Acad Sci U S A. 1986 Dec;83(23):8987-91 – Fig. 2 CCW vs CW bias for tethered cells in response to step in attractant

The chemotaxis network http://www.rowland.harvard.edu/labs/bacteria/projects_fret.html …but signal integration and sensitivity are still not well understood.

Chemoreceptors Dimer Tar - aspartate, glutamate (~900 copies) Tsr - serine (~1600) Trg - ribose, galactose (~150) Tap - dipeptides (~150) (Aer - oxygen via FAD (150?)) Sensor Transmembrane helices Linker region 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 380 A Methyl binding sites CheB, CheR Cytoplasmic domain CheA / CheW binding region Stock (2000)

Chemoreceptor clustering Receptors are clustered globally into a large array, and locally into trimers of dimers. Gestwicki et al. (2000) Gestwicki et al. J. Bacteriol. 182, 6499-6502 (2000) – Immunofluorescence images using anti-Trg antibody. Kim et al. (1999); Studdert and Parkinson (2004)

In vivo FRET studies of receptor activity Real-time measurement of rate of phosphorylation of CheY. FRET also allows subcellular imaging, Vaknin And Berg (2004). IMPORTANT ADVANTAGE OF FRET IS THAT CHEY-P IS UPSTREAM OF MOTOR. A. Vaknin and H. C. Berg, Single-cell FRET imaging of phosphatase activity in the Escherichia coli chemotaxis system, Proc Natl Acad Sci U S A. 2004 Dec 7;101(49):17072-7. Sourjik and Berg (2002)

FRET data: two regimes of activity Sourjik and Berg (2002) Regime I Regime II 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 C. A. Hale, H. Meinhardt, and P. A. J. de Boer, EMBO J. 20, 1563-1572 (2001) – Fig. 7. Two regimes of receptor activity consistent with 2-state receptor model.

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. Barkai and Leibler (1997)

Two regimes of a 2-state receptor On Off But first, a “1-state” receptor: Regime I Regime II Regime I: Activity low to very low at zero ligand concentration KD = KDoff Regime II: Activity high (saturated) at zero ligand concentration KD increasing as εon ↓ Off Off On On Free Energy Off Off C. A. Hale, H. Meinhardt, and P. A. J. de Boer, EMBO J. 20, 1563-1572 (2001) – Fig. 7. On KD Ligand Ligand Ligand However, single receptor does not account for low apparent KD in Regime I.

Receptor-receptor coupling Duke 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, Regime I (Δε > 0): Low activity ~ e-NΔε at zero ligand concentration KD = KDoff / N Hill coefficient = 1 Regime II (Δε < 0): KD = KDoff e-Δε Hill coefficient = N C. A. Hale, H. Meinhardt, and P. A. J. de Boer, EMBO J. 20, 1563-1572 (2001) – Fig. 7. Receptor-receptor coupling gives enhanced sensitivity (low KD) in Regime I, and enhanced cooperativity (high Hill coefficient ) in Regime II.

Review of FRET data 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 ? = KDoff /N, value of N ? C. A. Hale, H. Meinhardt, and P. A. J. de Boer, EMBO J. 20, 1563-1572 (2001) – Fig. 7. More Tars Less Tars Hill coefficient increases with receptor homogeneity. Must consider mixture of different receptor types. Sourjik and Berg (2004)

Model: 1d mixed lattice of receptors Tsr Tar EJ 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 Normalized Activity C. A. Hale, H. Meinhardt, and P. A. J. de Boer, EMBO J. 20, 1563-1572 (2001) – Fig. 7. Log([MeAsp])

Receptor homogeneity and cooperativity 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. Normalized Activity C. A. Hale, H. Meinhardt, and P. A. J. de Boer, EMBO J. 20, 1563-1572 (2001) – Fig. 7. Log([MeAsp]) More Tars Less Tars

Adaptation Adaptation uses methylation to return all receptors to Δε ≈ 0, and thereby enhances sensitivity. Tsr Tar Δε ≈ 0 Δε > 0 Δε ≈ 0 Δε > 0 Δε ≈ 0 Δε > 0 C. A. Hale, H. Meinhardt, and P. A. J. de Boer, EMBO J. 20, 1563-1572 (2001) – Fig. 7. Off Δε ≈ 0

Precise adaptation C. A. Hale, H. Meinhardt, and P. A. J. de Boer, EMBO J. 20, 1563-1572 (2001) – Fig. 7.

Scaling of wild-type response data Sourjik and Berg: Δ[MeAsp] → ΔFRET{Tar(QEQE)} “Free energy” scaling: Δ[MeAsp] → Δ(Fon – Foff) ΔFRET for Tar(QEQE) strain Sourjik and Berg (2002) C. A. Hale, H. Meinhardt, and P. A. J. de Boer, EMBO J. 20, 1563-1572 (2001) – Fig. 7. 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 Activity C. A. Hale, H. Meinhardt, and P. A. J. de Boer, EMBO J. 20, 1563-1572 (2001) – Fig. 7. MeAsp Sourjik (unpublished)

Open questions Lattice structure? Mechanism of receptor-receptor coupling? Do other receptors work this way? C. A. Hale, H. Meinhardt, and P. A. J. de Boer, EMBO J. 20, 1563-1572 (2001) – Fig. 7. Stock (2000)

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