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 logarithmic Caputo fractional derivative. We find an approximate analytical solution for this model which represents an upper bound for the fractional SI dynamics on a network. This upper bound is expressed in terms of the Mittag-Leffler function of the adjacency matrix of the network of inter-amino acids interactions. We consider some network descriptors based on these Mittaf-Leffler matrix functions which account for the "circulability" and "transmissibility" of the perturbations across the residues of a protein. We then apply this model and descriptors to the analysis of the communication effects produced by inhibitors of the main protease of COVID-19 . We find that the perturbation produced by strong inhibitors of the protease are propagated up to 60 \AA away from the binding site, confirming the long-range nature of intra-protein communication  . These findings may help to the design of drug candidates against this new coronavirus.
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.
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logarithmic Caputo fractional
Caputo fractional-order
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approximate analytical solution for
upper bound to the analytical solution of
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an upper bound for the fractional SI dynamics on a
the worse-case scenario on the propagation of perturbations across a protein residue
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the
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function
functions
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consider some network descriptors based on these Mittaf-Leffler matrix functions which account for the "circulability" and "transmissibility" of the perturbations across the residues of a protein. We
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and descriptors
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communication effects
propagation of perturbations
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COVID-19
SARS CoV-2
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perturbation
perturbations
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up to 60
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\AA
far
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. On the contrary, the weakest inhibitors only transmit their perturbations across a close environment around the binding site