Physical principles underpinning molecular-level protein evolution.

Since protein mutations are the main driving force of evolution at a molecular level, a proper analysis of the factors controlling them-such as the proteins' robustness, the evolutionary pathways, the number of ancestors, the epistasis, the post-translational modifications, and the location and the order of mutations-will enable us to find a response to several crucial queries in evolutionary biology. Among them, we highlight the following: At the molecular level, what factors determine whether protein evolution is repeatable? Aiming at finding an answer to this and several other significant questions behind protein evolvability, we distinguish two evolutionary models in our analysis: convergent and divergent, based on whether or not a "target sequence" needs to be reached after n mutational steps beginning with a wild-type protein sequence (from an unknown ancestor). Preliminary results suggest-regardless of whether the evolution is convergent or divergent-a tight relationship between the thermodynamic hypothesis (or Anfinsen's dogma) and the protein evolution at the molecular level. This conjecture will allow us to uncover how fundamental physical principles guide protein evolution and to gain a deeper grasp of mutationally driven evolutionary processes and the factors that influence them. Breaking down complex evolutionary problems into manageable pieces-without compromising the vision of the problem as a whole-could lead to effective solutions to critical evolutionary biology challenges, paving the way for further progress in this field.