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.

中文翻译：

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分数阶易感感染模型：定义及其在COVID-19主要蛋白酶研究中的应用


摘要：我们提出了一个模型，用于通过表示为相互作用网络的蛋白质氨基酸传递扰动。动力学由基于 Caputo 分数阶导数的易感感染 (SI) 模型组成。我们找到了该模型解析解的上限，它代表了扰动在蛋白质残基网络中传播的最坏情况。该上限以氨基酸间相互作用网络的邻接矩阵的 Mittag-Leffler 函数表示。然后，我们将该模型应用于分析 SARS CoV-2 主要蛋白酶抑制剂产生的扰动的传播。我们发现强蛋白酶抑制剂产生的扰动传播到远离结合位点的地方，证实了蛋白质内通讯的长程性质。相反，最弱的抑制剂仅将其扰动传递到结合位点周围的封闭环境中。这些发现可能有助于设计针对这种新型冠状病毒的候选药物。