Drag forces: What is the drag force of a 100nm vesicle when moving at a typical molecular motor velocity? (use the viscosity of the cytosol and look up motor speeds)
This is essentially the same as a previous excercise put with a 5 fold smaller radius. Hence the mobility is 5 fold lower and the force 5 fold higher.
$$ F \approx 20\times 0.1\mu m\times 0.2\mu m/s \times 10^{-3} pNs/\mu m^2 = 0.4\times 10^{-3} pN$$
Diffusion vs directed transport: What is the distance beyond which directed transport by a molecular motor is faster than diffusion for (i) a typical protein, (ii) a 1kb mRNA, (iii) a 100nm vesicle?
The time it takes to be carried by a motor a distance \(d\) is \(t = d/v\). We are hence looking for the distance where \(d = \sqrt{6Dd/v}\) or
$$ d = 6D/v \approx 12D \frac{s}{\mu m} $$
where I have assumed a motor speed of 550nm/s.