Abstract
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.
Acknowledgements
We thank the Editor and the three anonymous referees for useful suggestions that improve the presentation of this work.
The first author has been partly supported by Project MTM2016-77710-P, DGI-FEDER, of the MCYTS, Project E26-17R, D.G. Aragón, and Project for Young Researchers, Fundación Ibercaja and Universidad de Zaragoza, Spain.
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