APh161: The Physics of Biological Structure andFunctionHomework 4Due Date: Tuesday, Feb. 20, 2007“An ounce of application is worth a ton of abstraction.” - Booker T.WashingtonReading: Read chap. 9 of PBOC and write a referee report in the usualway. Please remember as you are doing this that this is a huge help to usas we try to improve the book for its eventual publication. We appreciate itvery much and it is a chance for you to construct a concrete written argument.1. Nucleosome Formation and AssemblyThe goal of this problem is for you to reexamine the ideas developed in classconcerning the assembly and accessibility of the nucleosome and to rederivethe expression for the DNA accessibility using a discrete model.(a) Repeat the derivation given in class and arrive at an expression forthe free energy of formation of nucleosomes. Make sure that you explain thequalitative features of the calculation and that you identify the numericaloutcome of the analysis (please report your energies in units of kBT ). In par-ticular, comment on the way in which you handle the elastic and interactioneffects and rationalize the energy per length that you assign to each of theseeffects. Also, instead of pretending that the DNA wraps around the nucle-osome fully two times, use the more precise description involving 147 basepairs of wrapped DNA leading to 1.75 wraps around the histones. A secondrefinement is to include the helical pitch of the DNA as it wraps around thenucleosome - here, just make an estimate to show that this refinement isnot very important. (Hint: to do this you will need to remember that thebending energy is of the formEbend=ξpkBT2Zdsκ(s)2, (1)1where κ(s) is the curvature. ) In addition, take a look at papers describingthe structure of the nucleosome (such as Nature, 389, 251 (1997); Nature423, 145 (2003); J. Mol. Bio. 319, 1097 (2002)) and make sure that youcharacterize the structural features of the nucleosome that you use in yourmodel.(b) In class, we examined the experiments of Polach and Widom (J. Mol.Biol., 254, 130, (1995)) which examined the equilibrium accessibility of dif-ferent sites within the nucleosome as a function of the distance within thenucleosome that the DNA binding site is buried. In this part of the problem,you will reexamine the derivation of the equilibrium accessibility and explic-itly compare your results with those of Polach and Widom. As I did in class,derive expressions for the fractional coverage of different sites as a functionof how deeply they are buried in the nucleosome and explain in detail thearguments leading to the result. Next, derive the equilibrium constant wecall Kconfeq(x) and compare your results explicitly to those from Polach andWidom. Make sure you are careful in describing the logic of reconciling themicroscopic model and the description in terms of equilibrium constants. Aspart of the procedure to compare to Polach and Widom, you will have to fitthe adhesive energy γ that I used to characterize the histone-DNA interac-tions.(c) Calculate the equilibrium accessibility assuming that there is a dis-crete number of contacts (N = 14). How does it compare to the continuummodel? Obtain the corresponding value of γdiscreteand plot the equilibriumaccessibility vs. burial depth for both models simultaneously.(d) Look at some of the binding affinities of different DNA sequences tohistones reported by Lowary and Widom (J. Mol. Biol. (1998) 276, 19). Aswe did in class and in the last two problems, assume that the electrostaticinteraction between the histone and the different DNA molecules does notvary, that it is not sequence dependent. This is equivalent to saying that thedifference between each sequence lies in its flexibility, in its bending energy.What would one expect the difference in their persistence lengths to
View Full Document
Unlocking...