The model we are going to build today comes from two research papers published about 20 years ago (note: you will need to be connected to MSU computer or wifi to access these articles)
http://www.nature.com/nature/journal/v390/n6656/full/390196a0.html
http://www.pnas.org/content/95/11/5872.full
A β-sheet is a basic unit of protein structure, and the smallest sheet is just two strands connected by a loop, making a hairpin. We are going to study a hairpin from a larger protein structure, the B1 domain of Streptococcal Protein G (the red and yellow strands in the picture below left).
As you can see in the picture, the structure is held in place by hydrogen bonds between opposite strands of the hairpin. There are also hydrophobic interactions between the hydrophobic residues. The bottom right figure shows all the interactions that hold the native structure together, the green dotted lines are hydrogen bonds and the blue dotted lines are hydrophobic interactions. To make the fully folded structure all these interactions have to be in place but we can also find out how many partially folded structures we can have with some of the interactions.
We can set up a model in which we count all the ways a protein chain can form this hairpin of parts of the hairpin. We will make a rule that only one contiguous stretch of hairpin is allowed because that will make counting all the combinations easier (fewer microstates). For example, the stretch DDATKT must have all the hydrogen bonds between D-T and D-K to called folded, otherwise it is unfolded. Then we need to choose how much entropy and enthalpy is gained or lost as each interaction is formed. Finally we can calculate the free energy for each arrangement of amino acids in the sequence as either folded or not folded. For any amino acids that are folded we calculate the change in enthalpy and entropy for making one or more interactions and add them up to get the total free energy for that conformation.
1) Make some of the conformations that might be included in the model. You can draw them as a structure (some of the hairpin) and also as a sequence of designated folded (F) and unfolded (U) amino acids. (e.g. UUUFFFFFFUUUUUUU). Remember don't include any structures/sequences that have two or more stretches of folded (e.g. UUUFFFFFFUUFFFFF). How many folded residues do you have? How many hydrogen bonds are made? How many hydrophobic interactions?
2) Go here to copy the code and paste into your Glowscript account.
3)Discuss with your group how each of the "for" loops work.
4)Put in the correct form of the Gibbs Free energy for each conformation. Discuss with your group which different enthalpies and entropies have to be included. Why does it get calculated when it does in the code? How do you account for all the interactions that exist for any particular conformation?
5) The correct values for each interaction per amino acid (from the papers listed above) are
delta_Hhb = -1.1 #in kcal/mol
delta_Gsc = -2.1 #in kcal/mol
delta_Sconf = -0.0032 #in kcal/(mol K)
Put these in and run the code. Discuss with your group what the two graphs show you. In particular look at the bottom plot: the colors of the circles measure the free energy with blue lowest and red highest. If you start at the bottom of the plot in the unfolded state, what is the most likely path to the top of the plot in the folded state? Which amino acids will fold first?
6) Try changing the values listed above slightly and see how that changes the free energy plots.
©Lisa J. Lapidus 2016