  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.
