Bacterial chemotaxis without gradient-sensing

Chemotaxis models are based on spatial or temporal gradient measurements by individual organisms. The key contribution of Keller and Segel (J Theor Biol 30:225–234, 1971a ; J Theor Biol 30:235–248, 1971b ) is showing that erratic measurements of individuals may result in an accurate chemotaxis phenomenon as a group. In this paper we provide another option to understand chemotactic behavior when individuals do not sense the gradient of chemical concentration by any means. We show that, if individuals increase their dispersal rate to find food when there is not enough food, an accurate chemotactic behavior may be obtained without sensing the gradient. Such a dispersal has been suggested by Cho and Kim (Bull Math Biol 75:845–870, 2013 ) and was called starvation driven diffusion. This model is surprisingly similar to the original Keller–Segel model. A comprehensive picture of traveling bands and fronts is provided.