Limits of Feedback Control in Bacterial Chemotaxis
Figure 6
Performance trade-off in bacterial chemotaxis.
A. Optimal adapted CheY-P concentrations Y0 (solution of Eqs (4) with 0→m and (5)) as a function of the chemoreceptor adaptation time in different exponential gradients (g−1 = 1,000 (red), 2,000 (green), and 5,000 (blue) µm). Dots indicate when the maximal theoretical drift velocities cross the bifurcation point (dotted lines represent the inaccessible optimal state). The optimal operational CheY-P concentration Ym is identical for all gradient length scales (black dashed line). B. Contour plot of drift velocities as a function of adaptation time and the adapted cell tumble bias in different exponential gradients (same colors as A). 75%, 90%, and 95% contours of the maximal theoretical drift velocities for each gradient (colors intensities from light to dark). Black dot: the best cell phenotype that achieves equal relative drift velocities in all three gradients (60% of the maximal VD with τ = 7.5 s and TB0 = 0.044).