Conclusion

Refinement of the methodologies of protein structure determination yielded a massive amount of important information about protein structure. Due to the fundamental developments in the field of molecular evolution, this information unveiled a peculiar picture of the protein structural, sequence, and functional spaces. In particular, graph-theoretical approaches enable us to decipher specific characteristics of these spaces.

It has been suggested25 that protein thermodynamics is one of the important evolutionary driving forces that shape the protein sequence space and govern the architecture of the protein structural space. This force relates protein sequence and structural spaces.

One striking observation is the scale-free organization of the PDUG8—protein structural space—which is signified by hierarchical relations between structurally similar proteins. The emergence of power-law scaling of the PDUG connectivity p (k) is the result of evolutionary dynamics that is as robust at the scale of specific proteomes or at the scale of all organisms. The correlation between structural organization of proteomes and appearance of new organisms (speciation)124 also suggest a truly universal "scale-free" evolutionary dynamics, whereby the appearance of new protein fold families is parallel to appearance of new species.

Distributions of function and structure over the PDUG act as two evolutionary lenses. It is evident that the evolution of structure and function is mutual and governed by the same underlying principles.135 Since according to divergent evolution, aside from the biochemical consideration of function structure correlation, there is also biological pressure for proteins to retain close functional as well as structural similarity to their ancestors upon mutation and duplication. This implies a possibility to trace protein lineages via structural comparisons and further identify a possible function of putative proteins.

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