(A) Magnified view of a migrating bacterial front from the simulation shown in Figure 2A at time min as a representative example. To illustrate the spatially varying nutrient levels, we show the contours of constant nutrient concentration and in magenta and cyan, respectively; these represent characteristic upper and lower limits of sensing. The contours are spaced closer at the leading edge of the convex peak () than the concave valley (), indicating that the magnitude of the local nutrient gradient is larger at peaks than at valleys. The nutrient concentration itself, which increases monotonically with increasing , is also larger at the peak than at the valley. (B) Top and bottom panels show the variation of the nutrient sensing function and chemotactic response function , respectively, with nutrient concentration . Because sensing saturates at high nutrient concentrations, chemotactic response is weaker at higher (peaks) than at lower (valleys). (C) Top panel shows the component of the nutrient gradient (red, left axis) and the response function (blue, right axis), and bottom panel shows the component of the chemotactic velocity computed from these quantities, evaluated at different lateral positions along the leading edge of the front in (A). While the driving force of chemotaxis represented by is smaller at the valley, the chemotactic response is larger at the valley and dominates in setting : valleys move out faster than peaks, eventually catching up to them and smoothing out the undulations. (D) For all simulations (Figure 2E), the smoothing time determined by analyzing the decay of large-scale undulations (Figure 2D) is similar to the time needed for valleys to catch up to peaks estimated using their different -component chemotactic velocities. Note that we do not expect an exact match between and as they are related yet different quantities.