A better model of a DNA molecule is the ‘one-dimensional freely jointed chain’, in which a rigid unit of length l can only make an angle of 0° or 180 ° with an adjacent unit. In this case, the restoring force of a chain extended by x=nl is given by

Where k is Boltzmann’s constant.

(a) What is the magnitude of the force that must be applied to extend a DNA molecule with N=200 by 90nm? 

(b) Plot the restoring force against ν, noting that ν can be either positive or negative. How is the variation of the restoring force with end-to-end distance different from that predicted by Hooke’s law?

(c) Keep in mind that the difference in end-to-end distance from an equilibrium value is x=nl and, consequently, dx=ldn=Nldν, and write an expression for the work of extending a DNA molecule.

(d) Calculate the work of extending a DNA molecule from ν=0 to ν=1.0.

You must integrate the expression for w. The task can be accomplished easily with mathematical software. 

Transcribed Image Text:

F= In F() V= n N