Advanced physics

The X chromosome in human cells consists of 20 MB of information encoded on N = 1.6 X 1|[II8 basepairs in a DNA double helix molecule. The information is processed as mechanisms open one end of the double helix molecule and break basepair bonds. Assume the opposite end remains closed and energy 8 is needed to break a single basepair. Index 3 (U :1 s i N) labels the site of a specific base pair starting from the opening end and pair 3 can break provided all pairs less than s are already broken (see figure for s = 6 below where dashed lines represent broken bonds}. Each broken bond pair along the molecular backbone can then adopt 6 possible orientations each of which are degenerate in energy {see curved arrows in figure for s' = 1}. (a) If the DNA molecule is in thermal equilibrium with the body at temperature T, explain which ensemble is appropriate to model the thermodynamics of this system. {b} Write down the appropriate partition function, Z, for the system in terms of the sum over microstates. [cl To first approximation, setting G = 1, determine an expression for the expected energy, >, ofthe molecule in the low temperature limit where T r: E/kB. {d} Hence find the expected number of broken bonds, > ? What does this imply for the stability of the DNA molecule in the body