Abstract
We examine the threshold of the influence of the tunneling nanotubes (TNTs) on the cell-to-cell communication integrity. A deterministic model is introduced with the Michaelis-Menten dynamics and the intercellular exchange of substance. The influence of TNTs are considered as a functional perturbation of the main communication and treated as the matrix nearness problems. We analyze communication integrity in terms of the \emph{pseudospectra} of the exchange, to find the \emph{distance to instability}. The threshold of TNTs influence is computed for Newman-Gastner and Erdős-Rényi gap junction (GJ) networks.
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