  In previous papers we have described with strong experimental support, the
organising role that CoHSI (Conservation of Hartley-Shannon Information) plays
in determining important global properties of all known proteins, from defining
the length distribution, to the natural emergence of very long proteins and
their relationship to evolutionary time. Here we consider the insight that
CoHSI might bring to a different problem, the distribution of identical
proteins across species. Horizontal and Vertical Gene Transfer (HGT/VGT) both
lead to the replication of protein sequences across species through a diversity
of mechanisms some of which remain unknown. In contrast, CoHSI predicts from
fundamental theory that such systems will demonstrate power law behavior
independently of any mechanisms, and using the Uniprot database we show that
the global pattern of protein re-use is emphatically linear on a log-log plot
(adj. $R^{2} = 0.99, p < 2.2 \times 10^{-16}$ over 4 decades); i.e. it is
extremely close to the predicted power law. Specifically we show that over 6.9
million proteins in TrEMBL 18-02 are re-used, i.e. their sequence appears
identically in between 2 and 9,812 species, with re-used proteins varying in
length from 7 to as long as 14,596 amino acids. Using (DL+V) to denote the
three domains of life plus viruses, 21,676 proteins are shared between two
(DL+V); 22 between three (DL+V) and 5 are shared in all four (DL+V). Although
the majority of protein re-use occurs between bacterial species those proteins
most frequently re-used occur disproportionately in viruses, which play a
fundamental role in this distribution.
  These results suggest that diverse mechanisms of gene transfer (including
traditional inheritance) are irrelevant in determining the global distribution
of protein re-use.
