Force on ends of DNA chain

1. The source code hw6/dna.py simulates a stiff chain, such as DNA, when a force is applied to molecule's ends. This has been studied extensively experimentally as can be seen here Links to an external site., here Links to an external site., and here Links to an external site..

There are three parameters that come into the experiment, the stiffness constant StiffnessConst, the external force, f_ext, and the chain length n. Keep the stiffness and chain length constant as given in the source file, and vary f_ext to measure the end to end distance.

You can add code to average the end to end distance. At the end of the attached code, the vector r_out[i] measures the position 0 < i < n. Taking the difference between the values at the two ends gives the instantaneous distance between the ends. Average this over a long enough time so as to get a good estimate for the average.

When you average this over time you should only start averaging after the system has equilibrated, i.e. the end to end distance has come close to its average value.

How does this compare with the experimental data, and the theoretical fit that they use?

2. As mentioned above, this experimental data is obtained with an optical trap. How does tethering the dna molecule to the optical trap affect the amount of Brownian motion?

3. The above is a model, not just for DNA, but any linear polymer with local stiffness.

• Give examples of other biological structures that are linear yet have some local stiffness.
• What causes chain stiffness in such molecules?
• Find examples where the above results of force versus extension, and other chain properties will be relevant and important biologically.