Condition for intracellular adaptive dynamics for chemotaxis.

Chemotaxis is ubiquitously performed by bacteria. They sense and move toward a region with a higher concentration of an attractive chemical by changing the rate of tumbling for random walk. We numerically studied several models with internal adaptive dynamics to examine the validity of the condition for chemotaxis proposed by Oosawa and Nakaoka [J. Theor. Biol. 66, 747 (1977)], which states that the time scale of tumbling frequency must be smaller than that of adaptation and greater than that of sensing. Suitable renormalization of the time scales showed that the condition holds for a variety of environments and for both short- and long-term behavior.