Proteins fold on millisecond to microsecond time scales. Cyrus Levinthal claimed that proteins could not possibly go from unfolded to folded state this fast if they sampled anywhere near all possible states. The average protein has approximately 300 amino acids and let us assume each peptide bond that connects two amino acids has two possible configurations given by two different possible angles of rotation. Assume that the different protein conformations differ only in the peptide bond rotational angles, and assume it takes ten femtoseconds (1 fs = 10-15 s) to sample each conformation. a) Using simple statistics, show that Prof. Levinthal was right and that protein folding actually would take far longer than our lifetimes if it required sampling of all possible conformations.
b) If random state sampling were the whole story, the outlook would be even bleaker than this simple picture, because in reality there are more than 2 possible orientations and many proteins are longer than 300 amino acids. Luckily for life, nature found a better way. The actual mechanism of protein folding is a hot topic in research today. One of the hypotheses is that subsections of a protein and their appropriate conformation and 'lock' into place. Imagine that the protein is divided up into 8 segments their connection mimics a bond, with two possible configurations. Now how long will it take to sample each conformation?
c) Now consider that each of the 8 segments can be arranged with three possible configurations. What % increase in time does a third configuration add, relative to your answer in part b?