Limits of Feedback Control in Bacterial Chemotaxis
Figure 3
Feedback of the behavior of cells swimming in exponential gradients onto the operational CheY-P concentration.
A. Temporal profiles of the average methyl-aspartate concentration encountered by cells swimming in a steep exponential gradient (g−1 = 1,000 µm). Different phenotypes are considered (solid black: Y0 = 2.4 µM, τ = 10 s, solid gray: Y0 = 2.4 µM, τ = 30 s, dotted black: Y0 = 3 µM, τ = 10 s) (the y-axis is on a log scale). B. Corresponding average CheY-P concentration as a function of time in these same cells C. Magnitude of the drop in average CheY-P activity (difference between adapted and operational CheY-P concentrations Ym -Y0) as a function of the drift velocity. Two different adaptation times are considered (black: τ = 10 s, grey: τ = 30 s). The gradient is the same gradient as in panel A. Dots are averages over 10,000 stochastic simulations for populations with different adapted CheY-P concentrations (Y0>2.4 µM in both cases). Lines are from Eq. (4). D. Drift velocity VD as a function of adapted CheY-P concentration, Y0 (filled circles), and operational CheY-P concentration, Ym (open circles) in stochastic simulations (average over 10,000 replicates for each circle, τ = 10 s). Ym is instantaneous CheY-P concentration averaged over the population while drifting between t = 60 and 300 s). Two exponential gradients of methyl-aspartate are considered (g−1 = 1,000 µm (black), 5,000 µm (grey)). Black arrow: cell population in blue in Figure 4C.