Question

Consider a bacterium (radius ~1 μm) swimming through water at a speed of 25 μm/s. (a) How much force do the flagella of the bacteria have to generate to maintain that speed? (b) The motor protein kinesin generates a force of 6 pN. Given that the viscosity of the cytoplasm is ~1000 times that of water (for large objects like organelles), how fast could a single kinesin molecule move a bacterium though the cytoplasm environment? Express your answer in μm/s.

Answer 1

Part 1

The viscosity of water is

Using Stoke's Law, the viscous force exerted by the water on the bacterium, and hence the forces the flagella have to generate to maintain a speed of is

Substituting our values, we get

Part 2

Here, we find out the velocity when the force due to the kinesin molecule is equal to viscous force due to cytoplasm.

Viscosity of cytoplasm is approximately

Therefore,