Limits of Feedback Control in Bacterial Chemotaxis
Figure 4
Behavioral feedback can create a chemotactic “trap”.
A. Analytical drift velocity, VD as a function of Ym (Eq. (3) with 0→m; solid line) and feedback of VD on Ym (Eq. (4), dashed line) (τ = 5 s, g−1 = 1,000 µm, Y0 = 2.7 µM). Steady state drift velocity (Ym = 2.48 µM, black circle). B. Same as panel A, but for cells with longer adaptation time and higher adapted CheY-P (τ = 30 s, Y0 = 3.5 µM). VD has three possible steady states: two stable (Ym2 = 2.1 µM and Ym1 = 3.49 µM (black dots)), and one unstable (Ym = 2.97 µM, white dot). C. Individual drift velocities (in the direction of the gradient) and root mean square displacements (perpendicular to the gradient) of two different populations of 10,000 simulated cells (blue: τ = 10 s, Y0 = 2.6 µM, red: τ = 30 s, Y0 = 3 µM). D. Average VD as a function of Y0 (filled circles) and Ym (open circles) for cells with a long adaptation time (τ = 30 s). Black arrow: cell population plotted in panel C (red).