2D HP model

1. An elegant model that captures a lot of the the physics of protein folding is a lattice model called the HP model Links to an external site. (see also these papers Links to an external site.. Proteins live on a lattice, in two dimensions, normally it's taken to be square. Polymers can't intersect themselves but interact by nearest neighbor interactions. Instead of 20 kinds of amino acids, this is simplified down to two, hydrophobic, "H", and polar, "P". Here Links to an external site. is a picture of the ground state of such a model.

The HP model can be used to understand the different intermediate states of a protein as it folds. On this paper Links to an external site., they consider a 13 length chain and study its folding kinetics. The ground state energy is -5, at for this sequence it is unique. However how unique are the higher energy states?

Using hw7/lat_prot_py_2d.py, you can run a simulation of this model and watch how it folds as it cools down. At the moment it'll stop if the energy goes below -4. The ground state is -5. If you change the line of code:

while beta < 10.0 and energy_min > -4:

so the the -4 becomes -3, it'll stop when it goes to -3 or below.

Try running the code multiple times and take screenshots of the configurations you find. Are the configurations that you find at different energies unique (up to rotation, and reflection)? What does this suggest about the number of intermediate states one has when a protein folds?

2. The HP model ignores many important interactions. Give some examples of other interactions that should be included for a more accurate model. Do you think that these interactions should qualitatively affect your conclusions concerning intermediate states?

3. What happens qualitatively to this model as a function of temperature if there are: (a) many intermediate states right above the ground state (b) few intermediate states right above the ground state?