On a Condition for Intracellular Adaptive Dynamics for Chemotaxis
  Microorganisms often perform chemotaxis, (i.e., sensing and moving toward a region with a higher concentration of an attractive chemical) by changing the rate of tumbling for random walk. We studied several models with internal adaptive dynamics numerically to examine the validity of the condition for chemotaxis proposed by Oosawa and Nakaoka, which states that the time scale of tumbling frequency is smaller than that of adaptation and greater than that of sensing. Suitably renormalizing the timescales showed that the condition holds for a variety of environments and for both short- and long-term behavior. 
Masayo Inoue and Kunihiko Kaneko