Transmembrane proteins are embedded in cell membranes. If one transmembrane prot

Question

Transmembrane proteins are embedded in cell membranes. If one transmembrane protein is pulled away from the cell membrane using a magnetic force microscope (reading material: pp. 18 of the text book), and the force required to extract this protein is: (f/pN) = 15(x/nm) + (x/nm)^2 where x is the distance between the protein and membrane. The protein is pulled from the fully embedded state (x_1 = 0) to fully unbinded state(x_2 = 5 nm) What is the work needed to extract this transmembrane protein? What would be the work (in Joule) needed to extract 1 mole of such transmembrane protein?

Explanation / Answer

given

f in pico newton = 15x + x^2 [ where x is in nano meter]

and x changes from xi = 0 to xf = 5 nm

so f = 15x + x^2

work done in displacing the protien by dx = dW = f*dx

dW = f*dx = (15x + x^2)dx

integrating total work from xi to xf

W = 7.5xf^2 + xf^3/3

so work in pico newton * nano meter = 10^-12*10^-9 = 10^-21 J is

W = 7.5*5^2 + 5^3/3 = 229.166 *10^-21 J

2.1 W = 229.166*10^-21 J

2.2 number of protiens in one mole, n = 6.62*10^23

work done for one mole = nW = 6.62*10^23*10^-21 = 151708.3333 J

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