Figure 4. Dispersion of the cell population (no pulse wave).

(Top) In this experiment, bacteria are cultivated at a concentration of 5.10⁸cells.ml⁻¹ in the same rich medium as in Fig. 3. After, they are resuspended in LB nutrient to an OD600 of 3.10⁸cells.ml⁻¹. We interpret the absence of pulse propagation as following. Bacteria are adapted to a rich environmnent before resuspension. Thus they are not able to sense small chemical uctuations necessary for clustering to occur when evolving in a relatively poor medium. (Bottom) Inuence of the internal processes stiffness. When the individual response function φ is not stiff, the effect of dispersion is too strong and no pulse wave propagates, as opposed to Fig. 3. Specific parameters are: δ = 10 and N ₀ = 10³. In mathematical models of bacterial chemotaxis, it is commonly accepted that adaptation of cells to large chemoattractant changes acts through the measurement of relative time variations: S ⁻¹ DS/Dt. In our context, this is to say that the stiffness parameter δ is proportional to the chemical level S. Hence after having dramatically changed the environment and before bacteria adapt themselves, we can consider that the response function φ is not stiff.