We can think of the end distance r as indicating a macrostate of the DNA. That...

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We can think of the end distance r as indicating a macrostate of the DNA. That is, there are many particular configurations of the DNA that can give the same distance r. But different distances r will have more or fewer individual configurations that give r, i.e., different numbers of microstates. For example: if the DNA is completely stretched out (r = length of DNA), are there more or fewer ways to do that compared to letting the ends stay close together? Make a drawing that goes with your thinking. 2) Now remember that the probability of a macrostate is proportional to its number of microstates, 2. Using the formula connecting entropy and probability, calculate the entropy of the DNA chain. 3) If we don't pull on the DNA (or keep F< 10 pN) then the covalent bonds between nucleotides don't stretch very much and we don't have to worry about the internal energy of the DNA. But it is useful to think of the DNA entropy as a type of energy because as we've seen previously, the DNA acts like a spring and you can do work on the chain by compressing or stretching it to change the entropy. (We will discuss this in more detail in the next unit). The entropic energy of a system generally is U = -TS Careful: the temperature T is actually irrelevant but is required in this equation simply to cancel out the T in the Boltzmann probability equation. (We'll talk more about what T means later when we fully discuss free energy where we carefully put together enthalpy and entropy). Find an expression for the entropic energy of the DNA chain. Rearrange this expression into a form that looks like the spring potential energy U-1/2 k stretch^2. What factors go into the spring stiffness k? 4) Using the spring stiffness k you determined in 3), find an expression for the associated spring force. Comparing to real DNA data: 5) In previous activities we considered DNA force vs extension data generated by optical trapping pulling experiments. Plotted below is some example data (same as previously). How does the model you have created using statistical physics methods compare to the data (qualitatively)? We can think of the end distance r as indicating a macrostate of the DNA. That is, there are many particular configurations of the DNA that can give the same distance r. But different distances r will have more or fewer individual configurations that give r, i.e., different numbers of microstates. For example: if the DNA is completely stretched out (r = length of DNA), are there more or fewer ways to do that compared to letting the ends stay close together? Make a drawing that goes with your thinking. 2) Now remember that the probability of a macrostate is proportional to its number of microstates, 2. Using the formula connecting entropy and probability, calculate the entropy of the DNA chain. 3) If we don't pull on the DNA (or keep F< 10 pN) then the covalent bonds between nucleotides don't stretch very much and we don't have to worry about the internal energy of the DNA. But it is useful to think of the DNA entropy as a type of energy because as we've seen previously, the DNA acts like a spring and you can do work on the chain by compressing or stretching it to change the entropy. (We will discuss this in more detail in the next unit). The entropic energy of a system generally is U = -TS Careful: the temperature T is actually irrelevant but is required in this equation simply to cancel out the T in the Boltzmann probability equation. (We'll talk more about what T means later when we fully discuss free energy where we carefully put together enthalpy and entropy). Find an expression for the entropic energy of the DNA chain. Rearrange this expression into a form that looks like the spring potential energy U-1/2 k stretch^2. What factors go into the spring stiffness k? 4) Using the spring stiffness k you determined in 3), find an expression for the associated spring force. Comparing to real DNA data: 5) In previous activities we considered DNA force vs extension data generated by optical trapping pulling experiments. Plotted below is some example data (same as previously). How does the model you have created using statistical physics methods compare to the data (qualitatively)?

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1 The entropy of the DNA chain is proportional to the number of molecules in the chain This means that the more nucleotides in the chain the more ways there are for the chain to be arranged and theref... View the full answer