1. Simplification is key!

2. Use 2D lattice model in part one. Brute force might just work,  
avoid complex algorithms, the problem is complex enough. The product 
of (complex problem)x(complex algorithm) is a killer. If brute force 
proves to be intractable, try generating a good sample of conformations 
using Monte Carlo. It is conceptually very simple.  

If you feel you do not want to program, consider making a physical
bead-on-strings model using colored beads of any sort threaded through. 
Explore various conformations in 2D following the same emergetic rules 
(qualitatively) as above. Arrive at conclusions about which configurations
in space might be energetically most preferable == lowest energy. 

3. Assume Asp, Arg, Lys, Glu, Asn, Ser, Gln == hydrophilic. See old hydrophobicity scale (Wiki). 

4. You want to generate compact and non-compact states to make sure the compact
ones have lower energy. 

5. Note that you have an Arg and an ASP in your sequence, and they are 
not adjacent. Will these want to be next to each other in space? 
How would you account for it in your energy function?  Note that these 
are not just hydrophilic, there is something else special about them. 

 

6. For the second part, construct analytical, differentiable 
functions z = z(x, y) [or z(r, phi) if you use cylindrical coordinates ]  
that produce "realistic looking" folding funnels 
(e.g.
http://wavefunction.fieldofscience.com/2011/06/protein-folding-funnel-and-its.html
)
with great many local minima.  In fact, you might want to start with 1D 
funnels y = y(x). 

Then think which of the "standard" 
minimization method(s) might work. I highly recommend that 
you buy "Numerical recipes in C" book -- a bible in this field. Most 
of these methods are implemented in Mathematica, you can test them out easily.
Do not code them yourselves, it will be a waste of time.  
Visualize results!  Start with the simplest, such as Newton or Steepest
descent. You want to make a list of 5-10, discuss their pros and cons, 
and test them out on your funnels. 

I suggest that you do 6) concurrently with the lattice models, that some people in the group work on 1-5, and the rest on 6. 

7. By the end of the day, you need to have a pretty good idea which method(s) might work within 
a month at most, to allow just enough time to learn how to run AMBER and
try to fold a real protein. 

8. I will prepare the unfolded protein in the correct input format for AMBER. 
Your goal is to figure out which method to use, what are the control
parameters, and how to run the code. Folding will be through trial and error: 
you will try several parameters to see which ones might work. So by 
this point you will need
to have a pretty good idea what is computationally reasonable on your
supercomputer, and which method(s) might work. There is no point wasting your
precious time [and contribute to global warming] by running 
algorithms that are apriori not good enough to handle the 
"grand challenge" of computational science. 

Specifically, several differentiable functional forms E(x_i,y_i,z_i) that 
define a realistic funnel as a function of atomic 
coordinates x_i,y_i,z_i i=1,N are
available in AMBER. You will not have 
to worry about coding up anything. You can test out a couple of options for 
E(x,y,z) [set by igb=5 or igb=8 parameter], 
and choose the specific minimization option and its parameters. But 
remember to compare energies of structures only within one or the 
other energy function, that is do not compare energy value from between 
igb5 to igb8.  
You will be visualizing the folding trajectories via VMD, checking your 
simulation outputs often.