Chapter 4, Problem 2E

Explanation of Solution

Formulating the problem:

• The question mentioned is raises many issues despite its humble origins as the scientifically important problem of protein design.
• There is a discrete assembly space in which the track is filled with pieces chose and a “joint angle” is used to determine the continuous configuration space at every place where two pieces are linked.
• Thus the user can define a state with a set of linked, oriented pieces and the associated joint angles in the range [10,0], and with a set of pieces that are unlinked.
• The joint angles and linkage exactly determines the physical layout of the track.
• The user can allow or disallow for layouts in which tracks are arranged like one above another.
• The evolution function includes terms for,
  • Number of pieces used,
  • Number of loose ends,
  • The degree of overlap.
• The user might include a penalty for the amount of deviation, and the deviation can be from 0-degree joint angles...