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Question: question 4 12 points biologists use gel electrophoresis to sort...

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Question 4 12 points Biologists use gel electrophoresis to sort DNA segments by size. DNA segments are placed at one end of a gel. DNA is negatively charged (with a charge of two electrons per base pair). When you run the gel you are generating an electric field by connecting anodes and cathodes at the ends of the gel. This causes the negatively charged DNA segments to move towards the positive electrode. After running the gel, smaller DNA segments have moved farther from the starting end. The overall theme for this question is: Why do the smaller DNA segments move farther? Start Position for all DNA Final Position Longer DNA Segment Final Position Shorter DNA Segment (a) Each base pair of a DNA molecule has a negative charge of -2e. Defining whatever variables you find appropriate, come up with an expression for: i) the total charge of a DNA segment of N base pairs (1 point) ii) the total mass of a DNA segment of N base pairs (1 point) (b) To understand how electrophoresis might work we will start with a simple model. We will ignore the gel and assume that the only force acting on the DNA segments is the electric force due to a constant electric field Starting with a free body diagram, produce an equation that describes how the electrostatic force acts on DNA segments of different sizes. Use Newtons 2 law to decide how this force would affect the motion of different-sized segments of DNA. Does this explain how electrophoresis separates DNA segments by size? (2 points) Continues on the next page...
(c) 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, I (ii) A compact sphere, where the radius increases slowly with the number of base pairs, (iii) A loose spherical coil, where the radius increases rapidly with the number of base pairs, r - a The value of the constant a is different in each case, but does not affect the result 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. (8 points)
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