Chemosensing in Escherichia coli: two regimes of two-state receptors

Abstract

The chemotaxis network in Escherichia coli is remarkable for its sensitivity to small relative changes in the concentrations of multiple chemical signals. We present a model for signal integration by mixed clusters of interacting two-state chemoreceptors. Our model results compare favorably to the results obtained by Sourjik and Berg with in vivo fluorescence resonance energy transfer. Importantly, we identify two distinct regimes of behavior, depending on the relative energies of the two states of the receptors. In regime I, coupling of receptors leads to high sensitivity, while in regime II, coupling of receptors leads to high cooperativity, i.e., high Hill coefficient. For homogeneous receptors, we predict an observable transition between regime I and regime II with increasing receptor methylation or amidation.

Fig. 1.

Response of receptor activity to step of attractant. (a) Response measured by FRET by Sourjik and Berg (12) to quantified steps of the attractant MeAsp. (b) Response of the mixed-cluster MWC model with equal contributions from 14, 15, and 16 receptor clusters, with binomial distributions of receptors at a Tar:Tsr ratio of 1:2, to steps of MeAsp. In all cases, we set K_a^off = 0.02 mM, K_a^on = 0.5 mM, K_s^off = 100 mM. All energies in thermal energy units k_BT. The experimental strains, and our corresponding choices of offset energies ɛ_a, ɛ_s, are as follows: •, wild-type, 0, 0; ▾, cheR mutant, 0.2, 0.2; ▵, cheRcheB mutants–Tar {EEEE}, 1.0, –1.5; ◇, Tar {QEEE}, 0.0, –1.5; □, Tar {QEQE}, −0.6, −1.5; ▿, Tar {QEQQ}, −1.1, −1.5. All lines are to guide the eye.

Fig. 2.

Two regimes of a two-state receptor. Representative energy-level diagrams for a single two-state receptor as a function of ligand concentration. The four possible states of the receptor are shown in Inset. Red curves (on) and blue curves (off) correspond to active and inactive configurations of the receptor, and the superscripts refer to no ligand bound (0) and ligand bound (L). Dotted lines, energy levels of the unbound receptor; solid curves, ligand-bound receptor; arrows, ligand concentrations when lowest free-energy states cross. (a) Regime I : In the absence of a ligand, the on-state free energy is above the off-state free energy; crossing occurs at [L] = K_d^off. (b) Regime II: In the absence of a ligand, the on-state free energy is below the off-state free energy; crossing occurs at [L] = K_d^off exp(E_off − E_on).

Fig. 3.

Effect of receptor homogeneity on response to attractant. (a) Response measured by FRET to steps of MeAsp in ref. . Nonadapting cheRcheB mutant strains were constructed with Tar receptor expression at zero (◇), one (•), two (▪), and six (▴) times wild-type levels. (b) Dose–response curves for the mixed-cluster MWC model to steps of MeAsp. Response curves are shown for Tar:Tsr ratios 0:1 (◇), 1:2 (•), 1:1 (▪), and 3:1 (▴) with all parameters the same as in Fig. 1b. All lines are to guide the eye.

Fig. 4.

Transition from regime I to regime II for homogeneous receptors. Response of homogeneous clusters of Tar receptors to steps of MeAsp within the MWC model. Dose–response curves (solid) and receptor-occupancy curves (dashed) are shown for Tar receptor methylation states EEEE, QEEE, QEQE, and QEQQ (left to right), where the Tar-receptor parameters and cluster sizes are those used in Fig. 1b. (Inset Upper) Adaptation of averaged activity is shown of a cluster Tar receptors exposed to two steps of MeAsp from 0 mM up to 1 mM at t = 30 s and then down to 0.01 mM at t = 90 s. (Inset Lower) Average methylation level of receptors. Averages are taken over 100 independent clusters of six Tar receptors. Details of the Barkai-Leibler-type adaptation model (15) are given in supporting information.

Fig. 5.

Free-energy scaling of wild-type response. Response measured by FRET to steps of MeAsp in ref. for wild-type adapted cells. (Left) Data are shown for addition (Lower) and subsequent removal (Upper) of MeAsp (with curves to guide the eye) for cells adapted at various ambient MeAsp concentrations (see Inset, units are in mM). (Right) Response curves are rescaled according to a free-energy model as described in supporting information. The parameters are the same as in Fig. 1b, K_a^off = 0.02 mM, K_a^on = 0.5 mM, K_s^off = 100 mM.