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Complexity and synchronization in the process of biochemical substance exchange in a diffusively coupled ring of cells. (English) Zbl 1397.92168

Summary: We numerically investigate a model of a diffusively coupled ring of cells. To model the dynamics of individuel cells we consider a map with cell affinity, which is a generalization of the logistic map. First, we study the basic features of a one-cell system in terms of the Lyapunov exponent, Sample entropy and Kolmogorov complexity. Second, we test the complexity of this generalized logistic map via an information measure based on Kolmogorov complexity using the Lempel-Ziv algorithm. We compute a complexity counter indicating the number of distinct patterns in the generalized logistic map time series. The number of patterns in the measured time series is shown to increase with time series length but has a saturation value within the logistic time series. Third, the notion of observational heterarchy, which is a perpetual negotiation process between the different levels of the description of phenomenon, is reviewed. We also study how the active coupling induced by observational heterarchy modifies the synchronization property of a model with \(N_c=80\) cells. We observe that heterarchy has a dynamic structure that emerges from the existence of internal observers that can perform reinterpretation when we define heterarchy as observational heterarchy. We show numerically that active coupling enhances the synchronization of biochemical substance exchange under several conditions of cell affinity.

MSC:

92C37 Cell biology
68Q25 Analysis of algorithms and problem complexity
92B25 Biological rhythms and synchronization
37M25 Computational methods for ergodic theory (approximation of invariant measures, computation of Lyapunov exponents, entropy, etc.)
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