We discuss the complexity of folding and designing proteins.

1. We're thinking about the Kinato puzzle.
   This has an obvious analogy to the folding of proteins:
   1. The minority triangles are hydrophobic, while the majority triangles are hydrophilic.
   2. The triangles represent rotamers, side-chains that can be oriented at various angles.
   3. Many features, of course, are not modeled, including important energetic and bonding features.
2. How difficult is this puzzle?
   1. Is it possible to solve the puzzle in a way to protects the hydrophobic triangles?
   2. Is this solution unique?
   3. Is it possible to fill a triangle?
   4. What other shapes are possible?
   5. Is it possible to incrementally attack the folding of the puzzle?
3. A review of the construction of proteins.
   1. First, proteins are stable and biologically significant polypeptides. There are many others, of course.
   2. The structure of the ribosome. Seems to facilitate the folding with the help of other macro-molecules (chaperones).
4. Theoretical models for problems.
   1. P. Those problems solvable in polynomial time.
   2. NP. Thoese problems that may be verified (whose certificate) may be checked) in polynomial time.
   3. NP-complete. The set of NP problems to which all other NP problems can be reduced in polynomial time. These problems are the hardest of the NP-problems; solution of any of them in polynomial time leads to a solution of any others in polynomial time.
   4. NP-hard. Optimization problems that are difficult.
5. Punch-line: protein design is NP-hard.

Resources needed for this class:

• A paper, Protein Design is NP-Hard, which outlines the discussion of this class.

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