Figure 1.
Adaptation reactions on the chemoreceptor lattice.
(A) Bacterial chemoreceptors assemble into trimers of dimers that organize to form a dense hexagonal lattice. Most chemoreceptors have tether and modification sites. In the model, the assistance neighborhood for a given receptor (red) consists of all the receptors accessible by its tether, here taken to be the six nearest dimers (light red) in addition to itself. Groups of six receptor dimers switch cooperatively between active (blue) and inactive (white) states according to a MWC model. (B) Modeled reactions between CheR and the chemoreceptors with corresponding rates. Binding rates to the modification site depend on the receptor activity a. CheR in the cytoplasmic bulk may bind either the tether or modification site of a receptor (blue arrows, rates and
respectively). Once bound to the tether or modification site it may respectively bind the modification site or tether of itself (red arrows, rates
and
respectively) or any other receptor within its assistance neighborhood (green arrows, rate
to bind the neighboring modification site and rate
to bind the neighboring tether). Black arrows denote unbinding and catalytic steps (catalytic rate kr; tether unbinding rate
; modification site unbinding rate
). CheB-P participates in analogous reactions. In the rates, superscripts m and t denote binding to the modification site and tether site, respectively. The subscripts r and b denote CheR and CheB reactions, respectively.
Figure 2.
Processive receptor methylation compromises adaptation and decreases signaling noise.
Compared are three simulated models of the chemotaxis adaptation system: M1 with assistance neighborhoods and efficient brachiation (black traces), M2 with no assistance neighborhoods or brachiation (light gray), and M3 with assistance neighborhoods but inefficient brachiation (dark gray). Methylation is more processive in M2 and M3 than in M1. As processivity increases, enzymes become more localized to receptors that are already highly methylated (CheR) or demethylated (CheB), limiting their effectiveness. (A) The kinetics of M1 were calibrated by comparison to population-level measurements (gray) [43]. The model was exposed to simulated time-varying exponential ramps of methyl-aspartate and the resulting steady-state activity a0 recorded (black). (B) Response to small (5 µM) and large (1 mM) MeAsp step stimulus at applied at t = 200 s as measured by receptor activity a(t). While all models adapt to the small stimulus (top), they fail to adapt precisely to the large stimulus (bottom). For the large stimulus, higher processivity leads to less precise adaptation with M1 performing best and M2 worst. Activities have been scaled and recentered with steady-state values at 0. (C) Increasing processivity also decreases the magnitude of fluctuations in a(t) in the adapted state around the mean value a0. Plotted is the variance σaa of a(t) and the noise relative to the mean output σa/a0 (inset) for different expression levels of the enzyme CheR. Fluctuations are largest in M1 and smallest in model M2.
Table 1.
Summary of numerical models.
Figure 3.
Spontaneous output of the bacterial chemotaxis system.
Results are from stochastic simulations of a chemotaxis model M1 with a hexagonal receptor lattice and explicit enzyme tethering and the model B1 with no tethering or lattice structure. (A) We sampled representative cells from a population in which the ratio CheR/CheB/chemoreceptors is maintained but the overall expression level varies. Stochastic simulation of model M1 (black) predicts that some cells in this population will exhibit especially large fluctuations σa/a0∼10%. The magnitude of fluctuations increases sharply as the level of protein expression decreases. Noise levels in M1 are significantly larger than in B1 (gray) at all expression levels. The horizontal axis is normalized by the most common expression level. (B) The variance σaa of fluctuations in receptor activity is shown as CheR is varied while all other proteins are expressed at their mean levels. The variance σaa is significantly greater in M1 (black, diamonds) than in B1 (gray, circles). The model M1 produces exceeding 7% of the mean level (black, inset), while noise in B1 remains less than ∼3% (gray, inset). The noise was increased in B2 by increasing the enzyme-receptor affinities tenfold (light gray) relative to B1. (C) M1 and the (black, diamonds) and B1 (gray, circles) also exhibit similar dependence of the mean receptor activity at steady state a0 on CheR count. The model B2 with higher enzyme-receptor affinities exhibits highly ultrasensitive dependence on the CheR count (light gray).
Figure 4.
Large fluctuations arise from the saturated kinetics of localized enzymes.
(A) Variance of receptor activity σaa at steady state is significantly larger for the analytical model with localization (black) than without localization (gray; analytical version of model B1) for all values of total CheR RTot. The analytical model with localization (inset, black) exhibits signaling noise with σa/a0 up to ∼7% while noise in the model with no localization (analytical version of B1) remains at or below 3% of the mean output (inset, gray). (B) Mean receptor activity a0 at steady state as a function of CheR to CheB ratio. When plotted as a function of the total CheR to total CheB ratio, a0 exhibits a similar relatively robust profile for both the analytical model with localization (black) and without localization (gray; analytical version of B1). In contrast the mean receptor activity is ultrasensitive to the ratio of the localized CheR to localized CheB-P counts (gray, dot-dashed), . (Inset) Variance in receptor activity σaa (black, solid) decomposed into components due to fluctuation in localized CheR (black, dashed), localized CheB (gray, dashed), and small intrinsic fluctuations in the methylation rates (gray, dot-dashed) as in Eq. (11). All quantities are plotted as functions of relative RTot. (C) In the stochastic simulation of M1, steady-state activity a0 also has ultrasensitive dependence on the ratio of tethered CheR/CheB-P (gray), despite the weak dependence on total CheR/CheB (black). (Inset) 500 s simulation trace of instantaneous mean receptor activity a(t) (black) and instantaneous localized CheR/CheB-P (gray), smoothed with a 30 s sliding window average. (D) Comparison of the dependence of a0 on localized CheR/CheB-P for the simulated models M1 (black), M2 (light gray), and M3 (dark gray) from Fig. 2. This dependence is significantly weaker for the more processive models.