Metabolic cost of motility in planktonic protists: Theoretical considerations on size scaling and swimming speed

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Abstract
The metabolic cost of swimming for planktonic protists is calculated, on theoretical grounds, from a simple model based upon Stokes' law. Energetic expenditure is scaled over both typically encountered size ranges (1–100 µm) and swimming speeds (100–5,000 µm/sec). In agreement with previous estimates for typical flagellates, these estimates generally suggest a low (<1%) cost for motility, related to total metabolic rate of growing cells. However, the cost of motility in small, fast-moving forms, such as some ciliates and flagellates, may be significant (1–10%) and even substantial (10–100%+) for certain species. In accordance with these predictions, many fast-moving ciliates restrict motility to bursts of activity or “jumps.” In the absence of a reduction in swimming speed or in the frequency of jumps, it is predicted that this relative cost of motility will be significantly increased in starving heterotrophs or light-limited autotrophs, if such cells reduce cell volumes and specific rates of respiration.

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