Mystery Molecule

1. Single Molecule Force Spectroscopy has been applied to many molecules such as RNA Links to an external site. to study the folding and unfolding of a single molecule. The ends of the molecule are attached, through intermediate stages, to optical traps and a varying force can be applied to the ends of them. As a result, one obtains data for the extension of the molecule as a function of the applied force.

One can keep the force on the ends constant and observe how the extension randomly changes with time to determine details of the internal state of a molecule.

• When you have many possible internal states of a molecule, does it make transitions with equal probability between them, or is there more structure to the kinetics?
• How can you relate the fraction of time spent in a one state versus another, to differences in free energy?

2. With this in mind, you can analyze some fake data for the extension as a function of time, to try to determine what you can about the internal states of the chain. The gzipped data, hw6/mystery.gz is there and you don't have to ungzip it, scipy with take care of that for you! Analyze this data to determine things such as

• (i) The number of metastable states the molecule explores.
• (ii) The allowed transitions between theses states.
• (iii) What can you say about the free energy differences between these states?

To aid in this, a script hw6/analyze_myst.py is also included. It does a low pass filter of the data and performs a histogram on it as well. You will have to adjust the cutoff for the low pass filter. Keep in mind that there is more to the kinetics than just analyzing the histogram and you should try to say as much as you can about transitions between states by looking over the data very carefully.

3. What does studying single molecule force spectroscopy tell you experimentally? Give an example of a system where employing this technique has led to useful results.