The energetics and scaling of search strategies in bacteria

The influence of body size on the energetic cost of movement is well studied in animals but has been rarely investigated in bacteria. Here, I calculate the cost of four chemotactic strategies for different-sized bacteria by adding the costs of their locomotion and reorientation. Size differences of 0.1 microm result in 100,000-fold changes in the energetic cost of chemotaxis. The exact cost for any given size is a nonlinear function of flagella length, the minimum speed necessary to detect and respond to a signal, and the gradient of the signal. These parameters are interlinked in such a way that body size and strategy are tightly coupled to particular environmental gradients, offering avenues for explaining and exploring diversity and competition. The analysis here has implications beyond bacteria. Power-law regression through the minimum costs of transport for different kinds of chemotaxis has the same slope as that for swimming animals, suggesting a universal allometric equation for all swimming organisms.