On 2013 Jul 01, Joshua L Cherry commented:

This paper argues that protein evolution proceeds in a particular way: changes to the protein surface occur, and these enable changes to the core. Such a process would be non-time-reversible: fixation of the back-mutation(s) of the core, followed by the thus enabled backward change in the surface, is precluded, or at least less likely. This would be odd long-term behavior in the presence of fixed selective constraints. Furthermore, it is not clear how such irreversibility could be detected by the methods employed. This interpretation of Fig. 4A requires either that our observations start at some special time in the evolutionary process, or that the long-term process is somehow different from the sum of its parts. This is particularly strange-seeming because the longer evolutionary distances correspond to greater distances backward in time from contemporary species to common ancestors.

The phenomenon in Fig. 4A is in fact expected as an artifact of saturation effects. Rapidly changing positions become subject to such effects at shorter overall distances than slowly changing positions. Because surface positions are on average more rapidly evolving than core positions, the form of the nonlinearities in Fig. 4A is expected even in the complete absence of surface-core interactions.

On 2013 Jul 01, Joshua L Cherry commented:

This paper argues that protein evolution proceeds in a particular way: changes to the protein surface occur, and these enable changes to the core. Such a process would be non-time-reversible: fixation of the back-mutation(s) of the core, followed by the thus enabled backward change in the surface, is precluded, or at least less likely. This would be odd long-term behavior in the presence of fixed selective constraints. Furthermore, it is not clear how such irreversibility could be detected by the methods employed. This interpretation of Fig. 4A requires either that our observations start at some special time in the evolutionary process, or that the long-term process is somehow different from the sum of its parts. This is particularly strange-seeming because the longer evolutionary distances correspond to greater distances backward in time from contemporary species to common ancestors.

The phenomenon in Fig. 4A is in fact expected as an artifact of saturation effects. Rapidly changing positions become subject to such effects at shorter overall distances than slowly changing positions. Because surface positions are on average more rapidly evolving than core positions, the form of the nonlinearities in Fig. 4A is expected even in the complete absence of surface-core interactions.