Limits of Feedback Control in Bacterial Chemotaxis
Figure 2
Simulated and theoretical drift velocity VD in exponential gradient of aspartate L0egx.
A. VD as a function of the adapted CheY-P concentration Y0, in a shallow gradient (L0 = 200 µM and g−1 = 5,000 µm) for cells with adaptation times τ = 5 (blue), 10 (green), and 30 seconds (red). VD is the average velocity of 10,000 identical cells between t = 60 and 300 seconds (dots: stochastic simulations; lines: analytical solution from Eq. (3); grey: motor CW bias response curve. B. Expected trajectories of CheY-P concentration Y(F(t)) for cells running in one dimension up (green) or down (red) in a gradient (integration of Eqs. (2) and (5), see Text S1; τ = 30 s, g−1 = 5,000 µm, Y(Fi) = 2.4 µM and 3 µM). Expected run, (dotted line), and tumble,
(dashed line), durations as a function of Y0. Expected run duration along a given direction τR0 = (2Dr+λR0)−1 (solid black line) is limited by rotational diffusion (Dr = 0.062 rad2 s−1). Grey: motor CW bias. C. Same as A (τ = 10 s) but with the rotational diffusion constant Dr = 0.031 (red), 0.062 (green), and 0.124 (blue) rad2 s−1. Dotted lines: expected run duration in a given direction. D. Same as A (τ = 10 s) but with the motor switching rate ω = 2.6 (red), 1.3 (green), and 0.65 (blue) s−1. Dotted lines: expected run duration in a given direction.