6.1.P9
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Various components in a cell are moved through the cell by motor proteins such as kinesin. The kinesin attaches itself on one end to the packet it is moving (the "cargo" shown here as a big sphere) and the other end to a tubule (at the bottom of the picture). The kinesin has two "feet" at the bottom that detach, swing forward, and attach again alternately, "walking" the kinesin along the tubule. The cargo it's dragging is not moving in a vacuum, but is moving through a storm of wildly fluctuating fluid molecules (the water and other chemicals of which the fluid in the cell is made). This means that to drag the object through the fluid – even at a constant speed – the kinesin has to put in energy to counteract the resistive force of the fluid. It does so by burning ATP into ADP.
1. Suppose the packet being dragged through the cell's fluid has a mass, m, and, when it is moving through the fluid with a speed, v, experiences a viscous force of magnitude f = bv. Let's make a simple model of how this works in order to get a sense of scale. If the kinesin is exerting a constant force, Fk, on the cargo, which of the following expresses the condition on the two forces in order that the cargo move at a constant velocity? |
Source: The Inner Life of a Cell by Cellular Visions and Harvard University |
a) Fk > bv
b) Fk = bv
c) Fk < bv
2. How much work does the kinesin have to do in order to move the cargo a distance Δ along the tubule? Express your answer in terms of Δx and the symbols used in part 1.
3. Using your result from 2, create an expression for the rate at which work is done by the kinesin, ΔW/Δt.
4, A kinesin that is transporting a secretory vesicle uses approximately 80 ATP molecules/s. Each ATP provides a kinesin molecule with an energy of about 0.8 x 10-19 J. If the velocity of the kinesin is 800 nm/s, can you determine the force the kinesin is exerting, if you assume that all the ATP energy is used (100% efficiency)? If you can, find it. If not, explain why not.
Joe Redish 12/16/16