CS321 Project 2: Due in-class, December 3
The design and folding of model proteins
We consider a protein chain in two dimensions embedded in a square lattice. The chain
length is 16 and the sequence consists of eight Hs and eight Ps.
1. Pick your favorite shape on the two-dimensional square lattice (make sure it is a
chain of length 16 and has at least eight contacts). A contact is defined when the
two amino acid are separated by one lattice spacing and are not covalently linked.
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 contacts 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 16 (eight Hs
and eight 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 structure, a bond to be rotated and the direction (+/-) to perform the
rotation. It returns the modified structure.
7. Write a Matlab program that performs an optimization of a structure. Use a
straight line to represent a starting point for chain optimization in the Monte Carlo
search. Use the sequence that you optimized in (5).
8. Generate 10 folding trajectories (a trajectory = a Markov chain in time for
sequential 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!