A better analogy. Let’s say that 777777777 has a specific function X, and 333333333 has function Y. And let’s say you can mutate to be something like 777777377. It retains function X despite the mutation (functional robustness, which is observed in proteins), but it now it does a bit of function Y (functional promiscuity, which is also a property seen in proteins). By continuous mutations it becomes more specialized until it becomes 333333333.
That way, proteins are able to traverse the fitness landscape of the sequence space, while in a non-directed manner, it nevertheless allows for the discovery of new fitness peaks. Here below is a real life example. Take your time to comprehend the illustration.
Duplication events and changes in specificity and activity during the evolution of Saccharomyces cerevisiae MALS enzymes.The hydrolytic activity of seven modern MAL and IMA enzymes and of key ancestral enzymes (prefix anc) is given. The width of the colored bands corresponds to the k cat/K m-value of the enzyme for a specific substrate. For details see Voordeckers et al. (2012).


Ancestral protein reconstruction: techniques and applications
Ancestral sequence reconstruction (ASR) is the calculation of ancient protein sequences on the basis of extant ones. It is most powerful in combination with the experimental characterization of the corresponding proteins. Such analyses allow for the...