Chemotaxis: the role of internal delays

When exposed to certain chemoattractants, bacteria like Escherichia coli move up the concentration gradient delc with a velocity kdelc. Microscopically, E. coli moves at constant speed when it's flagellum is rotating counter-clockwise (ccw) and tumbles when the rotation is clockwise (cw). The lifetime of a ccw Interval, tau(+), is a function of the concentration c(t') experienced at earlier times. The corresponding response function was measured long ago by Berg and co-workers. We present here a detailed description of the motion taking place during one ccw interval. This gives an explicit formula relating the chemotactic coefficient kappa to the response function, the formula has some surprising features.