CS321 Project 2: Due in-class, December 6

The design and folding of model proteins

We consider a protein chain in two dimensions embedded in a square lattice. The chain length is 12 and the sequence consists of seven Hs and five Ps.
  1. Pick your favorite shape on the two-dimensional square lattice (make sure it is a chain of length 12 and has at least five contacts).
  2. Write a Matlab function that performs sequence shuffling. The function receives a sequence (e.g. HPHPHPHPHPHH) and returns a sequence in which one of pairs is permuted (e.g. the first pair is permuted -- PHHPHPHPHPHH).
  3. Write a Matlab function that evaluates the energy of a sequence in your favorite shape. It accepts as an input the sequence and the shape and returns the value of the energy. Remember, a contact between H-H contributes -1 to the energy while the conta cts H-P or P-P contribute zero.
  4. Write a Matlab function that makes Metropolis selection. It accepts a new and old energy values, and the temperature. It returns an accept/reject flag.
  5. Use Monte Carlo procedure to design an optimal sequence of length 12 (seven Hs and five Ps) for your favorite structure. The temperature should be reduced linearly starting from T = (Emax - Emin)/2. Repeat the sequence optimization at least 10 times. Check that you obtain the same sequence, or a sequence close in energy to the optimal energy. Use Markov chains of 10,000 steps.
  6. Write a Matlab function that performs 90 degrees rotation around selected bonds. It accepts a shape, a bond to be rotated and the direction (+/-) to perform the rotation. It returns the modified structure.
  7. Write a Matlab program that performs optimization of structure. Use a straight line to represent the chain as a starting point in the Monte Carlo search. Use the sequence that you optimized in (5).
  8. Generate 10 folding trajectories (trajectory = a Markov chain for structural changes). Do the trajectories converge to the correct structure at zero temperature? Tune the simulation parameters (number of steps, selection of bonds to be rotated) to obtain optimal structures as quickly as possible. It is nice if the solution converges to optimal structure but it is not guaranteed.
  9. Create a movie that displays the folding pathway (the corresponding Markov chain) from a straight line to a low energy structure.
Include a hard and electronic copy of all your Matlab programs with sample inputs and outputs. Good luck!