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Question: in reality the gel exerts a significant drag force on...

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In reality the gel exerts a significant drag force on the DNA segments. Drag forces are proportional to the cross-sectional area of an object, as we saw last semester. Here we want to learn something about the structure of DNA in solution based on the behavior observed in the electrophoresis gel. We will choose between three models for the structure of DNA that describe how its size and shape change with the number of base pairs:

(i) A long stiff rod, where the length increases in proportion to the number of base pairs, l = aN.

(ii) A compact sphere, where the radius increases slowly with the number of base pairs, r = aN1/3.

(iii) A loose spherical coil, where the radius increases rapidly with the number of base pairs, r = aN3/5. The value of the constant a is different in each case, but does not affect the result.

(iv) Use a free body diagram to analyze the forces acting on the DNA segments. Find an equation that describe the terminal speed, v, of the DNA is related to the number of base pairs in a DNA segment for each model above. Which model agrees with the results seen during electrophoresis?

Ask yourself based on the equations how the terminal speed changes with the number of base pairs N in the DNA. Hint: You will have to describe both the charge and the cross-sectional area of the DNA in terms of the number of base pairs N.

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