Thus, to assess the difficulty of a random search, it’s necessary to know how many of the combinations will open the lock. The key isn’t just the number of total combinations that have to be searched, but the ratio of the number of combinations that will open the lock to the total number of combinations. In the same way, it isn’t just the total number of possible combinations in the amino-acid sequence space that determines the difficulty of a random search for a new protein structure. Ultimately, it’s the ratio of functional to nonfunctional sequences that determines the difficulty.
