Chemotaxis: the role of internal delays

When exposed to certain chemoattractants, bacteria like Escherichia coli move up the concentration gradient[Delta inverted]c with a velocity kappa[delta inverted]c. 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.