Minimum size limit for useful locomotion by free-swimming microbes

Formulas are derived for the effect of size on a free-swimming microbe's ability to follow chemical, light, or temperature stimuli or to disperse in random directions. The four main assumptions are as follows: (i) the organisms can be modeled as spheres, (ii) the power available to the organism for swimming is proportional to its volume, (iii) the noise in measuring a signal limits determination of the direction of a stimulus, and (iv) the time available to determine stimulus direction or to swim a straight path is limited by rotational diffusion caused by Brownian motion. In all cases, it is found that there is a sharp size limit below which locomotion has no apparent benefit. This size limit is estimated to most probably be about 0.6 micron diameter and is relatively insensitive to assumed values of the other parameters. A review of existing descriptions of free-floating bacteria reveals that the smallest of 97 motile genera has a mean length of 0.8 micron, whereas 18 of 94 nonmotile genera are smaller. Similar calculations have led to the conclusion that a minimum size also exists for use of pheromones in mate location, although this size limit is about three orders of magnitude larger. In both cases, the application of well-established physical laws and biological generalities has demonstrated that a common feature of animal behavior is of no use to small free-swimming organisms.