分数阶传染病模型的定义及其在COVID-19主要蛋白酶研究中的应用
Fractional-order susceptible-infected model: definition and applications to the study of COVID-19 main protease
摘要：
我们提出了一个模型的传输扰动整个氨基酸的蛋白质表示为一个相互作用网络。动力学由基于Caputo分数阶导数的易感感染（SI）模型组成。我们找到了这个模型的解析解的上限，它代表了蛋白质残基网络中扰动传播的最坏情况。该上限用氨基酸间相互作用网络的邻接矩阵的Mittag-Leffler函数表示。然后，我们应用这个模型来分析传播的扰动抑制剂的主要蛋白酶的SARS冠状病毒-2。我们发现，由强抑制剂的蛋白酶产生的扰动传播远离结合位点，证实了蛋白质内通信的长程性质。相反，最弱的抑制剂仅在结合位点周围的封闭环境中传递其扰动。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。
英文摘要：
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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