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Hysteresis in Single Molecule Force Spectroscopy

"Single Molecule Force Spectroscopy" has a term coined to describe the manipulation of the ends of a single molecule in order to probe properties of its structure. It is a rapidly developing technique that has been applied to many molecules such as RNA Links to an external site. to study the folding and unfolding of a single RNA molecule.

The ends of the molecule are attached, via "handles", to optical traps and an external force can be applied to the ends of them with great precision. As a result, one obtains data for the extension of the molecule as a function of the applied force.

What has been often noticed is that as the force is increased and then decreased, the extension depends on the history of the system. This can be used to understand details of the internal states of the system. As a simple example consider the simulation attached here. It models a molecule as a set of inextensible links, with some bending stiffness, and thermal noise. Two groups are added to the chain that have an attractive interaction separated by 8 links. This leads to an attractive force. In the attached code this is called in the function bind_force().

  • 1. From the form given for the force in function bind_force, calculate the corresponding potential energy of attraction of the two groups.
  • 2. Run the code hw6/twostatechain.py. You will see that the force applied is ramped up and then ramped down again.  Change tot_time to make it longer as well.  After a few minutes graphs will appear. One is the distance between the two groups as a function of force. You will notice that that graph shows hysteresis. f_incr controls the rate at which the force is incremented as the simulation is run. What happens to the graph if you increase f_incr? Can you understand the results? (Note: due to a recently introduced incompatibility, to see the graphs at the end, you need to set graphics = False)
  • 3. Try changing the temperature T from 1 to 0. What happens to the hysteresis curve? Can you understand your results?
  • 4. You can keep the force constant by running the code hw6/twostatechain_std_st.py and watch as chain conformations vary. However you have to wait a long time relative to the simulation you have just been running. Perhaps up to 30 minutes. When you do this, you can look at the graph of the distance as a function of time, t. What does this graph tell you?
  • 5. Compare these results to the Figure 1 of the above paper of Woodside et al Links to an external site..
  • 6. Suppose you consider a large RNA molecule, with more than 1000 bases, in this situation where you can apply a variable force and observe its overall extension. In general, do you expect just a few distinct states to be present or many?
  • 7. What are the limitations on how well the structure of RNA can be determined? Are there any ways that you can think of to increase the ability to determine the pattern of folding?
  • 8. What is hysteresis? What is its biological relevance, that is what does it tell you about the biology or biochemistry of the system?
  • 9. Aside from hysteresis in single molecules, what are other systems that show hysteresis?

 

UPDATE:

Due to changes in SciPy and Visual Python, the code you have won't show plots at the end. To get this to work, download the appropriate version here Links to an external site., and set graphics = False.