  We propose a model for the transmission of perturbations across the amino
acids of a protein represented as an interaction network. The dynamics consists
of a Susceptible-Infected (SI) model based on the Caputo fractional-order
derivative. We find an upper bound to the analytical solution of this model
which represents the worse-case scenario on the propagation of perturbations
across a protein residue network. This upper bound is expressed in terms of
Mittag-Leffler functions of the adjacency matrix of the network of inter-amino
acids interactions. We then apply this model to the analysis of the propagation
of perturbations produced by inhibitors of the main protease of SARS CoV-2. We
find that the perturbations produced by strong inhibitors of the protease are
propagated far away from the binding site, confirming the long-range nature of
intra-protein communication. On the contrary, the weakest inhibitors only
transmit their perturbations across a close environment around the binding
site. These findings may help to the design of drug candidates against this new
coronavirus.
